{"id":2623,"date":"2026-01-09T16:07:40","date_gmt":"2026-01-09T10:37:40","guid":{"rendered":"https:\/\/www.manabadi.co.in\/boards\/?p=2623"},"modified":"2026-01-09T16:07:44","modified_gmt":"2026-01-09T10:37:44","slug":"ts-inter-1st-year-maths-1a-solutions-cp-3-matrices-ex-3a","status":"publish","type":"post","link":"https:\/\/www.manabadi.co.in\/boards\/ts-inter-1st-year-maths-1a-solutions-cp-3-matrices-ex-3a\/","title":{"rendered":"TS Inter 1st Year Maths 1A Solutions Chapter 3 Matrices Ex 3(a)"},"content":{"rendered":"\n<h2>TS Inter 1st Year Maths 1A Matrices Solutions Exercise 3(a)<\/h2>\n\n<h3>Question 1.<br> Write the following as a single matrix.<br> (i) [2 1 3] + [0 0 0]<br> Answer:<br> [2 1 3] + [0 0 0] = [2 + 0 1 + 0 3 + 0]<br> = [2 1 3]<\/p>\n\n<p>(ii) <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-1-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-1\" style=\"width: 8.297em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 7.132em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.192em, 1006.81em, 6.247em, -999.998em); top: -4.471em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-2\"><span class=\"mrow\" id=\"MathJax-Span-3\"><span class=\"mo\" id=\"MathJax-Span-4\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-5\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-6\"><span class=\"mrow\" id=\"MathJax-Span-7\"><span class=\"mn\" id=\"MathJax-Span-8\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-9\"><span class=\"mrow\" id=\"MathJax-Span-10\"><span class=\"mn\" id=\"MathJax-Span-11\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-12\"><span class=\"mrow\" id=\"MathJax-Span-13\"><span class=\"mo\" id=\"MathJax-Span-14\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-15\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-16\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-17\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mrow\" id=\"MathJax-Span-18\" style=\"padding-left: 0.235em;\"><span class=\"mo\" id=\"MathJax-Span-19\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-20\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-21\"><span class=\"mrow\" id=\"MathJax-Span-22\"><span class=\"mo\" id=\"MathJax-Span-23\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-24\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-25\"><span class=\"mrow\" id=\"MathJax-Span-26\"><span class=\"mn\" id=\"MathJax-Span-27\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-28\"><span class=\"mrow\" id=\"MathJax-Span-29\"><span class=\"mn\" id=\"MathJax-Span-30\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-31\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-1\">\\left[\\begin{array}{r}  0 \\\\  1 \\\\  -1  \\end{array}\\right]+\\left[\\begin{array}{r}  -1 \\\\  1 \\\\  0  \\end{array}\\right]<\/script><br> Answer:<br> <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-2-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-32\" style=\"width: 8.297em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 7.132em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.192em, 1006.81em, 6.247em, -999.998em); top: -4.471em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-33\"><span class=\"mrow\" id=\"MathJax-Span-34\"><span class=\"mo\" id=\"MathJax-Span-35\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-36\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-37\"><span class=\"mrow\" id=\"MathJax-Span-38\"><span class=\"mn\" id=\"MathJax-Span-39\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-40\"><span class=\"mrow\" id=\"MathJax-Span-41\"><span class=\"mn\" id=\"MathJax-Span-42\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-43\"><span class=\"mrow\" id=\"MathJax-Span-44\"><span class=\"mo\" id=\"MathJax-Span-45\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-46\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-47\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-48\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mrow\" id=\"MathJax-Span-49\" style=\"padding-left: 0.235em;\"><span class=\"mo\" id=\"MathJax-Span-50\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-51\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-52\"><span class=\"mrow\" id=\"MathJax-Span-53\"><span class=\"mo\" id=\"MathJax-Span-54\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-55\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-56\"><span class=\"mrow\" id=\"MathJax-Span-57\"><span class=\"mn\" id=\"MathJax-Span-58\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-59\"><span class=\"mrow\" id=\"MathJax-Span-60\"><span class=\"mn\" id=\"MathJax-Span-61\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-62\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-2\">\\left[\\begin{array}{r}  0 \\\\  1 \\\\  -1  \\end{array}\\right]+\\left[\\begin{array}{r}  -1 \\\\  1 \\\\  0  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-3-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-63\" style=\"width: 5.454em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.709em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1004.38em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-64\"><span class=\"mrow\" id=\"MathJax-Span-65\"><span class=\"mo\" id=\"MathJax-Span-66\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-67\"><span style=\"display: inline-block; position: relative; width: 3.031em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.425em, 1002.99em, 6.247em, -999.998em); top: -4.564em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 3.031em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.19em, 4.243em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-68\"><span class=\"mrow\" id=\"MathJax-Span-69\"><span class=\"mn\" id=\"MathJax-Span-70\" style=\"font-family: MathJax_Main;\">0<\/span><span class=\"mo\" id=\"MathJax-Span-71\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-72\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.19em, 4.243em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-73\"><span class=\"mrow\" id=\"MathJax-Span-74\"><span class=\"mn\" id=\"MathJax-Span-75\" style=\"font-family: MathJax_Main;\">1<\/span><span class=\"mo\" id=\"MathJax-Span-76\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mn\" id=\"MathJax-Span-77\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.99em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-78\"><span class=\"mrow\" id=\"MathJax-Span-79\"><span class=\"mo\" id=\"MathJax-Span-80\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-81\" style=\"font-family: MathJax_Main;\">1<\/span><span class=\"mo\" id=\"MathJax-Span-82\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mn\" id=\"MathJax-Span-83\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-84\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-3\">\\left[\\begin{array}{r}  0-1 \\\\  1+1 \\\\  -1+0  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-4-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-85\" style=\"width: 3.404em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.938em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1002.61em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-86\"><span class=\"mrow\" id=\"MathJax-Span-87\"><span class=\"mo\" id=\"MathJax-Span-88\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-89\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-90\"><span class=\"mrow\" id=\"MathJax-Span-91\"><span class=\"mo\" id=\"MathJax-Span-92\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-93\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-94\"><span class=\"mrow\" id=\"MathJax-Span-95\"><span class=\"mn\" id=\"MathJax-Span-96\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-97\"><span class=\"mrow\" id=\"MathJax-Span-98\"><span class=\"mo\" id=\"MathJax-Span-99\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-100\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-101\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-4\">\\left[\\begin{array}{r}  -1 \\\\  2 \\\\  -1  \\end{array}\\right]<\/script><\/p><p>(iii) <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-5-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-102\" style=\"width: 13.795em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 11.885em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1011.65em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-103\"><span class=\"mrow\" id=\"MathJax-Span-104\"><span class=\"mo\" id=\"MathJax-Span-105\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-106\"><span style=\"display: inline-block; position: relative; width: 4.289em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-107\"><span class=\"mrow\" id=\"MathJax-Span-108\"><span class=\"mn\" id=\"MathJax-Span-109\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-116\"><span class=\"mrow\" id=\"MathJax-Span-117\"><span class=\"mn\" id=\"MathJax-Span-118\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.942em, -999.998em); top: -4.005em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-110\"><span class=\"mrow\" id=\"MathJax-Span-111\"><span class=\"mn\" id=\"MathJax-Span-112\" style=\"font-family: MathJax_Main;\">9<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-119\"><span class=\"mrow\" id=\"MathJax-Span-120\"><span class=\"mn\" id=\"MathJax-Span-121\" style=\"font-family: MathJax_Main;\">8<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1001.21em, 4.988em, -999.998em); top: -4.005em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-113\"><span class=\"mrow\" id=\"MathJax-Span-114\"><span class=\"mn\" id=\"MathJax-Span-115\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-122\"><span class=\"mrow\" id=\"MathJax-Span-123\"><span class=\"mo\" id=\"MathJax-Span-124\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-125\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-126\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-127\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mrow\" id=\"MathJax-Span-128\" style=\"padding-left: 0.235em;\"><span class=\"mo\" id=\"MathJax-Span-129\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-130\"><span style=\"display: inline-block; position: relative; width: 3.497em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.942em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-131\"><span class=\"mrow\" id=\"MathJax-Span-132\"><span class=\"mn\" id=\"MathJax-Span-133\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-140\"><span class=\"mrow\" id=\"MathJax-Span-141\"><span class=\"mn\" id=\"MathJax-Span-142\" style=\"font-family: MathJax_Main;\">7<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-134\"><span class=\"mrow\" id=\"MathJax-Span-135\"><span class=\"mn\" id=\"MathJax-Span-136\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-143\"><span class=\"mrow\" id=\"MathJax-Span-144\"><span class=\"mn\" id=\"MathJax-Span-145\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-137\"><span class=\"mrow\" id=\"MathJax-Span-138\"><span class=\"mn\" id=\"MathJax-Span-139\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-146\"><span class=\"mrow\" id=\"MathJax-Span-147\"><span class=\"mn\" id=\"MathJax-Span-148\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-149\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-5\">\\left[\\begin{array}{ccc}  3 & 9 & 0 \\\\  1 & 8 & -2  \\end{array}\\right]+\\left[\\begin{array}{ccc}  4 & 0 & 2 \\\\  7 & 1 & 4  \\end{array}\\right]<\/script><\/h3>\n\n<p>Answer:<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5651\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-1.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-1\" width=\"217\" height=\"165\" data-pin-nopin=\"true\"><\/p>\n\n<p>(iv) <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-6-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-150\" style=\"width: 12.724em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 10.953em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.192em, 1010.63em, 6.247em, -999.998em); top: -4.471em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-151\"><span class=\"mrow\" id=\"MathJax-Span-152\"><span class=\"mo\" id=\"MathJax-Span-153\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-154\"><span style=\"display: inline-block; position: relative; width: 3.544em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-155\"><span class=\"mrow\" id=\"MathJax-Span-156\"><span class=\"mo\" id=\"MathJax-Span-157\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-158\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-162\"><span class=\"mrow\" id=\"MathJax-Span-163\"><span class=\"mn\" id=\"MathJax-Span-164\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-169\"><span class=\"mrow\" id=\"MathJax-Span-170\"><span class=\"mn\" id=\"MathJax-Span-171\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-159\"><span class=\"mrow\" id=\"MathJax-Span-160\"><span class=\"mn\" id=\"MathJax-Span-161\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-165\"><span class=\"mrow\" id=\"MathJax-Span-166\"><span class=\"mo\" id=\"MathJax-Span-167\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-168\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-172\"><span class=\"mrow\" id=\"MathJax-Span-173\"><span class=\"mo\" id=\"MathJax-Span-174\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-175\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-176\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-177\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mrow\" id=\"MathJax-Span-178\" style=\"padding-left: 0.235em;\"><span class=\"mo\" id=\"MathJax-Span-179\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-180\"><span style=\"display: inline-block; position: relative; width: 2.798em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-181\"><span class=\"mrow\" id=\"MathJax-Span-182\"><span class=\"mn\" id=\"MathJax-Span-183\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-187\"><span class=\"mrow\" id=\"MathJax-Span-188\"><span class=\"mo\" id=\"MathJax-Span-189\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-190\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-194\"><span class=\"mrow\" id=\"MathJax-Span-195\"><span class=\"mo\" id=\"MathJax-Span-196\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-197\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-184\"><span class=\"mrow\" id=\"MathJax-Span-185\"><span class=\"mn\" id=\"MathJax-Span-186\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-191\"><span class=\"mrow\" id=\"MathJax-Span-192\"><span class=\"mn\" id=\"MathJax-Span-193\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; right: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-198\"><span class=\"mrow\" id=\"MathJax-Span-199\"><span class=\"mn\" id=\"MathJax-Span-200\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-201\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-6\">\\left[\\begin{array}{rr}  -1 & 2 \\\\  1 & -2 \\\\  3 & -1  \\end{array}\\right]+\\left[\\begin{array}{rr}  0 & 1 \\\\  -1 & 0 \\\\  -2 & 1  \\end{array}\\right]<\/script><br>\n\nAnswer:<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5652\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-2.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-2\" width=\"272\" height=\"162\" data-pin-nopin=\"true\"><\/p>\n\n<h3>Question 2.<br> If A = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-7-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-202\" style=\"width: 4.942em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.243em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1004.01em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-203\"><span class=\"mrow\" id=\"MathJax-Span-204\"><span class=\"mo\" id=\"MathJax-Span-205\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-206\"><span style=\"display: inline-block; position: relative; width: 2.798em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1001.21em, 4.895em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-207\"><span class=\"mrow\" id=\"MathJax-Span-208\"><span class=\"mo\" id=\"MathJax-Span-209\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-210\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-214\"><span class=\"mrow\" id=\"MathJax-Span-215\"><span class=\"mn\" id=\"MathJax-Span-216\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-211\"><span class=\"mrow\" id=\"MathJax-Span-212\"><span class=\"mn\" id=\"MathJax-Span-213\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-217\"><span class=\"mrow\" id=\"MathJax-Span-218\"><span class=\"mn\" id=\"MathJax-Span-219\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-220\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-7\">\\left[\\begin{array}{cc}  -1 & 3 \\\\  4 & 2  \\end{array}\\right]<\/script>, B = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-8-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-221\" style=\"width: 4.942em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.243em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1004.01em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-222\"><span class=\"mrow\" id=\"MathJax-Span-223\"><span class=\"mo\" id=\"MathJax-Span-224\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-225\"><span style=\"display: inline-block; position: relative; width: 2.798em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.942em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-226\"><span class=\"mrow\" id=\"MathJax-Span-227\"><span class=\"mn\" id=\"MathJax-Span-228\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-232\"><span class=\"mrow\" id=\"MathJax-Span-233\"><span class=\"mn\" id=\"MathJax-Span-234\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1001.21em, 4.988em, -999.998em); top: -4.005em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-229\"><span class=\"mrow\" id=\"MathJax-Span-230\"><span class=\"mn\" id=\"MathJax-Span-231\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-235\"><span class=\"mrow\" id=\"MathJax-Span-236\"><span class=\"mo\" id=\"MathJax-Span-237\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-238\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-239\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-8\">\\left[\\begin{array}{cc}  2 & 1 \\\\  3 & -5  \\end{array}\\right]<\/script>, X = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-9-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-240\" style=\"width: 5.268em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.522em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1004.29em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-241\"><span class=\"mrow\" id=\"MathJax-Span-242\"><span class=\"mo\" id=\"MathJax-Span-243\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-244\"><span style=\"display: inline-block; position: relative; width: 3.078em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.798em, 1001.03em, 5.082em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1001.03em, 4.289em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-245\"><span class=\"mrow\" id=\"MathJax-Span-246\"><span class=\"msubsup\" id=\"MathJax-Span-247\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1000.61em, 4.15em, -999.998em); top: -4.005em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-248\"><span class=\"mrow\" id=\"MathJax-Span-249\"><span class=\"mi\" id=\"MathJax-Span-250\" style=\"font-family: MathJax_Main-bold;\">x<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; top: -3.865em; left: 0.608em;\"><span class=\"mn\" id=\"MathJax-Span-251\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1<\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.404em, 1001.03em, 4.336em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-259\"><span class=\"mrow\" id=\"MathJax-Span-260\"><span class=\"msubsup\" id=\"MathJax-Span-261\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1000.61em, 4.15em, -999.998em); top: -4.005em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-262\"><span class=\"mrow\" id=\"MathJax-Span-263\"><span class=\"mi\" id=\"MathJax-Span-264\" style=\"font-family: MathJax_Main-bold;\">x<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; top: -3.865em; left: 0.608em;\"><span class=\"mn\" id=\"MathJax-Span-265\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">3<\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.798em, 1001.03em, 5.035em, -999.998em); top: -4.005em; left: 2.053em;\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1001.03em, 4.289em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-252\"><span class=\"mrow\" id=\"MathJax-Span-253\"><span class=\"msubsup\" id=\"MathJax-Span-254\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1000.61em, 4.15em, -999.998em); top: -4.005em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-255\"><span class=\"mrow\" id=\"MathJax-Span-256\"><span class=\"mi\" id=\"MathJax-Span-257\" style=\"font-family: MathJax_Main-bold;\">x<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; top: -3.865em; left: 0.608em;\"><span class=\"mn\" id=\"MathJax-Span-258\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">2<\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.404em, 1001.03em, 4.289em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-266\"><span class=\"mrow\" id=\"MathJax-Span-267\"><span class=\"msubsup\" id=\"MathJax-Span-268\"><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.404em, 1000.61em, 4.15em, -999.998em); top: -4.005em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-269\"><span class=\"mrow\" id=\"MathJax-Span-270\"><span class=\"mi\" id=\"MathJax-Span-271\" style=\"font-family: MathJax_Main-bold;\">x<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; top: -3.865em; left: 0.608em;\"><span class=\"mn\" id=\"MathJax-Span-272\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">4<\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-273\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-9\">\\left[\\begin{array}{ll}  \\mathbf{x}_1 & \\mathbf{x}_2 \\\\  \\mathbf{x}_3 & \\mathbf{x}_4  \\end{array}\\right]<\/script> and A + B = X then find the values of x<sub>1<\/sub>, x<sub>2<\/sub>, x<sub>3<\/sub> and x<sub>4<\/sub>.<\/h3>\n\n<p>Answer:<br> A + B = X<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5638\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-3.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-3\" width=\"295\" height=\"183\" data-pin-nopin=\"true\"><br> \u21d2 x<sub>1<\/sub> = 1, x<sub>2<\/sub> = 4, x<sub>3<\/sub> = 7, x<sub>4<\/sub> = \u2013 3.<\/p>\n\n<h3>Question 3.<br> If A = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-10-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-274\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-275\"><span class=\"mrow\" id=\"MathJax-Span-276\"><span class=\"mo\" id=\"MathJax-Span-277\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-278\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-279\"><span class=\"mrow\" id=\"MathJax-Span-280\"><span class=\"mo\" id=\"MathJax-Span-281\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-282\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-290\"><span class=\"mrow\" id=\"MathJax-Span-291\"><span class=\"mn\" id=\"MathJax-Span-292\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-299\"><span class=\"mrow\" id=\"MathJax-Span-300\"><span class=\"mn\" id=\"MathJax-Span-301\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-283\"><span class=\"mrow\" id=\"MathJax-Span-284\"><span class=\"mo\" id=\"MathJax-Span-285\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-286\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-293\"><span class=\"mrow\" id=\"MathJax-Span-294\"><span class=\"mn\" id=\"MathJax-Span-295\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-302\"><span class=\"mrow\" id=\"MathJax-Span-303\"><span class=\"mo\" id=\"MathJax-Span-304\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-305\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 4.569em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-287\"><span class=\"mrow\" id=\"MathJax-Span-288\"><span class=\"mn\" id=\"MathJax-Span-289\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-296\"><span class=\"mrow\" id=\"MathJax-Span-297\"><span class=\"mn\" id=\"MathJax-Span-298\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-306\"><span class=\"mrow\" id=\"MathJax-Span-307\"><span class=\"mn\" id=\"MathJax-Span-308\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-309\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-10\">\\left[\\begin{array}{ccc}  -1 & -2 & 3 \\\\  1 & 2 & 4 \\\\  2 & -1 & 3  \\end{array}\\right]<\/script> B = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-11-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-310\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-311\"><span class=\"mrow\" id=\"MathJax-Span-312\"><span class=\"mo\" id=\"MathJax-Span-313\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-314\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-315\"><span class=\"mrow\" id=\"MathJax-Span-316\"><span class=\"mn\" id=\"MathJax-Span-317\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-325\"><span class=\"mrow\" id=\"MathJax-Span-326\"><span class=\"mn\" id=\"MathJax-Span-327\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-335\"><span class=\"mrow\" id=\"MathJax-Span-336\"><span class=\"mn\" id=\"MathJax-Span-337\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.06em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-318\"><span class=\"mrow\" id=\"MathJax-Span-319\"><span class=\"mo\" id=\"MathJax-Span-320\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-321\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-328\"><span class=\"mrow\" id=\"MathJax-Span-329\"><span class=\"mo\" id=\"MathJax-Span-330\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-331\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-338\"><span class=\"mrow\" id=\"MathJax-Span-339\"><span class=\"mn\" id=\"MathJax-Span-340\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.26em, 6.247em, -999.998em); top: -4.564em; left: 3.777em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-322\"><span class=\"mrow\" id=\"MathJax-Span-323\"><span class=\"mn\" id=\"MathJax-Span-324\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-332\"><span class=\"mrow\" id=\"MathJax-Span-333\"><span class=\"mn\" id=\"MathJax-Span-334\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.26em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-341\"><span class=\"mrow\" id=\"MathJax-Span-342\"><span class=\"mo\" id=\"MathJax-Span-343\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-344\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-345\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-11\">\\left[\\begin{array}{ccc}  1 & -2 & 5 \\\\  0 & -2 & 2 \\\\  1 & 2 & -3  \\end{array}\\right]<\/script> and C = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-12-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-346\" style=\"width: 6.945em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 5.967em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1005.64em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-347\"><span class=\"mrow\" id=\"MathJax-Span-348\"><span class=\"mo\" id=\"MathJax-Span-349\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-350\"><span style=\"display: inline-block; position: relative; width: 4.289em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-351\"><span class=\"mrow\" id=\"MathJax-Span-352\"><span class=\"mo\" id=\"MathJax-Span-353\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-354\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-361\"><span class=\"mrow\" id=\"MathJax-Span-362\"><span class=\"mn\" id=\"MathJax-Span-363\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-370\"><span class=\"mrow\" id=\"MathJax-Span-371\"><span class=\"mn\" id=\"MathJax-Span-372\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-355\"><span class=\"mrow\" id=\"MathJax-Span-356\"><span class=\"mn\" id=\"MathJax-Span-357\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-364\"><span class=\"mrow\" id=\"MathJax-Span-365\"><span class=\"mn\" id=\"MathJax-Span-366\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-373\"><span class=\"mrow\" id=\"MathJax-Span-374\"><span class=\"mn\" id=\"MathJax-Span-375\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 3.777em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-358\"><span class=\"mrow\" id=\"MathJax-Span-359\"><span class=\"mn\" id=\"MathJax-Span-360\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-367\"><span class=\"mrow\" id=\"MathJax-Span-368\"><span class=\"mn\" id=\"MathJax-Span-369\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-376\"><span class=\"mrow\" id=\"MathJax-Span-377\"><span class=\"mn\" id=\"MathJax-Span-378\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-379\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-12\">\\left[\\begin{array}{ccc}  -2 & 1 & 2 \\\\  1 & 1 & 2 \\\\  2 & 0 & 1  \\end{array}\\right]<\/script> then find A + B + C.<\/h3>\n\n<p>Answer:<br> A + B + C =<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5637\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-4.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-4\" width=\"312\" height=\"250\"  sizes=\"auto, (max-width: 312px) 100vw, 312px\" data-pin-description=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-4\" data-pin-title=\"TS Inter 1st Year Maths 1A Solutions Chapter 3 Matrices Ex 3(a)\"><\/p>\n\n<h3>Question 4.<br> If A = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-13-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-380\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-381\"><span class=\"mrow\" id=\"MathJax-Span-382\"><span class=\"mo\" id=\"MathJax-Span-383\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-384\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-385\"><span class=\"mrow\" id=\"MathJax-Span-386\"><span class=\"mn\" id=\"MathJax-Span-387\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-395\"><span class=\"mrow\" id=\"MathJax-Span-396\"><span class=\"mn\" id=\"MathJax-Span-397\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-405\"><span class=\"mrow\" id=\"MathJax-Span-406\"><span class=\"mn\" id=\"MathJax-Span-407\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-388\"><span class=\"mrow\" id=\"MathJax-Span-389\"><span class=\"mn\" id=\"MathJax-Span-390\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-398\"><span class=\"mrow\" id=\"MathJax-Span-399\"><span class=\"mo\" id=\"MathJax-Span-400\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-401\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-408\"><span class=\"mrow\" id=\"MathJax-Span-409\"><span class=\"mn\" id=\"MathJax-Span-410\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.06em, -999.998em); top: -4.471em; left: 3.777em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-391\"><span class=\"mrow\" id=\"MathJax-Span-392\"><span class=\"mo\" id=\"MathJax-Span-393\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-394\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-402\"><span class=\"mrow\" id=\"MathJax-Span-403\"><span class=\"mn\" id=\"MathJax-Span-404\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-411\"><span class=\"mrow\" id=\"MathJax-Span-412\"><span class=\"mn\" id=\"MathJax-Span-413\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-414\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-13\">\\left[\\begin{array}{ccc}  3 & 2 & -1 \\\\  2 & -2 & 0 \\\\  1 & 3 & 1  \\end{array}\\right]<\/script>, B = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-14-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-415\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-416\"><span class=\"mrow\" id=\"MathJax-Span-417\"><span class=\"mo\" id=\"MathJax-Span-418\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-419\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.26em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.26em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-420\"><span class=\"mrow\" id=\"MathJax-Span-421\"><span class=\"mo\" id=\"MathJax-Span-422\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-423\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-431\"><span class=\"mrow\" id=\"MathJax-Span-432\"><span class=\"mn\" id=\"MathJax-Span-433\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-440\"><span class=\"mrow\" id=\"MathJax-Span-441\"><span class=\"mn\" id=\"MathJax-Span-442\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-424\"><span class=\"mrow\" id=\"MathJax-Span-425\"><span class=\"mo\" id=\"MathJax-Span-426\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-427\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-434\"><span class=\"mrow\" id=\"MathJax-Span-435\"><span class=\"mn\" id=\"MathJax-Span-436\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-443\"><span class=\"mrow\" id=\"MathJax-Span-444\"><span class=\"mo\" id=\"MathJax-Span-445\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-446\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 4.569em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-428\"><span class=\"mrow\" id=\"MathJax-Span-429\"><span class=\"mn\" id=\"MathJax-Span-430\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-437\"><span class=\"mrow\" id=\"MathJax-Span-438\"><span class=\"mn\" id=\"MathJax-Span-439\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-447\"><span class=\"mrow\" id=\"MathJax-Span-448\"><span class=\"mn\" id=\"MathJax-Span-449\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-450\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-14\">\\left[\\begin{array}{ccc}  -3 & -1 & 0 \\\\  2 & 1 & 3 \\\\  4 & -1 & 2  \\end{array}\\right]<\/script> and X = A + B then find X.<\/h3>\n\n<p>Answer:<br> X = A + B<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5636\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-5.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-5\" width=\"338\" height=\"163\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" data-pin-nopin=\"true\"><\/p>\n\n<h3>Question 5.<br> If <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-15-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-451\" style=\"width: 8.716em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 7.505em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1007.27em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-452\"><span class=\"mrow\" id=\"MathJax-Span-453\"><span class=\"mo\" id=\"MathJax-Span-454\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-455\"><span style=\"display: inline-block; position: relative; width: 6.06em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1002.29em, 4.988em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 2.332em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.29em, 4.243em, -999.998em); top: -4.658em; left: 50%; margin-left: -1.163em;\"><span class=\"mtd\" id=\"MathJax-Span-456\"><span class=\"mrow\" id=\"MathJax-Span-457\"><span class=\"mi\" id=\"MathJax-Span-458\" style=\"font-family: MathJax_Math-italic;\">x<\/span><span class=\"mo\" id=\"MathJax-Span-459\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-460\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.15em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-467\"><span class=\"mrow\" id=\"MathJax-Span-468\"><span class=\"mi\" id=\"MathJax-Span-469\" style=\"font-family: MathJax_Math-italic;\">z<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-470\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mn\" id=\"MathJax-Span-471\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1002.71em, 4.942em, -999.998em); top: -4.005em; left: 3.311em;\"><span style=\"display: inline-block; position: relative; width: 2.752em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.71em, 4.336em, -999.998em); top: -4.658em; left: 50%; margin-left: -1.349em;\"><span class=\"mtd\" id=\"MathJax-Span-461\"><span class=\"mrow\" id=\"MathJax-Span-462\"><span class=\"mn\" id=\"MathJax-Span-463\" style=\"font-family: MathJax_Main;\">2<\/span><span class=\"mi\" id=\"MathJax-Span-464\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-465\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-466\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">8<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-472\"><span class=\"mrow\" id=\"MathJax-Span-473\"><span class=\"mn\" id=\"MathJax-Span-474\" style=\"font-family: MathJax_Main;\">6<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-475\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-15\">\\left[\\begin{array}{cc}  x-3 & 2 y-8 \\\\  z+2 & 6  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-16-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-476\" style=\"width: 6.992em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.014em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1005.78em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-477\"><span class=\"mrow\" id=\"MathJax-Span-478\"><span class=\"mo\" id=\"MathJax-Span-479\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-480\"><span style=\"display: inline-block; position: relative; width: 4.569em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1001.21em, 4.988em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-481\"><span class=\"mrow\" id=\"MathJax-Span-482\"><span class=\"mn\" id=\"MathJax-Span-483\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-487\"><span class=\"mrow\" id=\"MathJax-Span-488\"><span class=\"mo\" id=\"MathJax-Span-489\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-490\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1002.24em, 4.988em, -999.998em); top: -4.005em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 2.286em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-484\"><span class=\"mrow\" id=\"MathJax-Span-485\"><span class=\"mn\" id=\"MathJax-Span-486\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1002.24em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-491\"><span class=\"mrow\" id=\"MathJax-Span-492\"><span class=\"mi\" id=\"MathJax-Span-493\" style=\"font-family: MathJax_Math-italic;\">a<\/span><span class=\"mo\" id=\"MathJax-Span-494\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-495\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-496\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-16\">\\left[\\begin{array}{cc}  5 & 2 \\\\  -2 & a-4  \\end{array}\\right]<\/script> then find the values of x, y, z and a. [May 2006, Mar. 14]<\/h3>\n\n<p>Answer:<br> Given <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-17-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-497\" style=\"width: 8.716em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 7.505em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1007.27em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-498\"><span class=\"mrow\" id=\"MathJax-Span-499\"><span class=\"mo\" id=\"MathJax-Span-500\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-501\"><span style=\"display: inline-block; position: relative; width: 6.06em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1002.29em, 4.988em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 2.332em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.29em, 4.243em, -999.998em); top: -4.658em; left: 50%; margin-left: -1.163em;\"><span class=\"mtd\" id=\"MathJax-Span-502\"><span class=\"mrow\" id=\"MathJax-Span-503\"><span class=\"mi\" id=\"MathJax-Span-504\" style=\"font-family: MathJax_Math-italic;\">x<\/span><span class=\"mo\" id=\"MathJax-Span-505\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-506\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.15em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-513\"><span class=\"mrow\" id=\"MathJax-Span-514\"><span class=\"mi\" id=\"MathJax-Span-515\" style=\"font-family: MathJax_Math-italic;\">z<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-516\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">+<\/span><span class=\"mn\" id=\"MathJax-Span-517\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1002.71em, 4.942em, -999.998em); top: -4.005em; left: 3.311em;\"><span style=\"display: inline-block; position: relative; width: 2.752em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.71em, 4.336em, -999.998em); top: -4.658em; left: 50%; margin-left: -1.349em;\"><span class=\"mtd\" id=\"MathJax-Span-507\"><span class=\"mrow\" id=\"MathJax-Span-508\"><span class=\"mn\" id=\"MathJax-Span-509\" style=\"font-family: MathJax_Main;\">2<\/span><span class=\"mi\" id=\"MathJax-Span-510\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-511\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-512\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">8<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-518\"><span class=\"mrow\" id=\"MathJax-Span-519\"><span class=\"mn\" id=\"MathJax-Span-520\" style=\"font-family: MathJax_Main;\">6<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-521\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-17\">\\left[\\begin{array}{cc}  x-3 & 2 y-8 \\\\  z+2 & 6  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-18-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-522\" style=\"width: 6.992em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.014em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1005.78em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-523\"><span class=\"mrow\" id=\"MathJax-Span-524\"><span class=\"mo\" id=\"MathJax-Span-525\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-526\"><span style=\"display: inline-block; position: relative; width: 4.569em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1001.21em, 4.988em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-527\"><span class=\"mrow\" id=\"MathJax-Span-528\"><span class=\"mn\" id=\"MathJax-Span-529\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-533\"><span class=\"mrow\" id=\"MathJax-Span-534\"><span class=\"mo\" id=\"MathJax-Span-535\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-536\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1002.24em, 4.988em, -999.998em); top: -4.005em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 2.286em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-530\"><span class=\"mrow\" id=\"MathJax-Span-531\"><span class=\"mn\" id=\"MathJax-Span-532\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1002.24em, 4.243em, -999.998em); top: -3.26em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-537\"><span class=\"mrow\" id=\"MathJax-Span-538\"><span class=\"mi\" id=\"MathJax-Span-539\" style=\"font-family: MathJax_Math-italic;\">a<\/span><span class=\"mo\" id=\"MathJax-Span-540\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-541\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-542\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-18\">\\left[\\begin{array}{cc}  5 & 2 \\\\  -2 & a-4  \\end{array}\\right]<\/script><br> We have x \u2013 3 = 5, 2y \u2013 8 = 2, z + 2 = \u2013 2, a \u2013 4 = 6<br> \u21d2 x = 8, y = 5, z = \u2013 4, a = 10<\/p>\n\n<h3>II.<br> Question 1.<br> If <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-19-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-543\" style=\"width: 12.164em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 10.487em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1010.16em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-544\"><span class=\"mrow\" id=\"MathJax-Span-545\"><span class=\"mo\" id=\"MathJax-Span-546\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-547\"><span style=\"display: inline-block; position: relative; width: 8.809em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1002.24em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 2.332em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -1.163em;\"><span class=\"mtd\" id=\"MathJax-Span-548\"><span class=\"mrow\" id=\"MathJax-Span-549\"><span class=\"mi\" id=\"MathJax-Span-550\" style=\"font-family: MathJax_Math-italic;\">x<\/span><span class=\"mo\" id=\"MathJax-Span-551\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-552\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-561\"><span class=\"mrow\" id=\"MathJax-Span-562\"><span class=\"mn\" id=\"MathJax-Span-563\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-572\"><span class=\"mrow\" id=\"MathJax-Span-573\"><span class=\"mn\" id=\"MathJax-Span-574\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1002.15em, 6.107em, -999.998em); top: -4.471em; left: 3.311em;\"><span style=\"display: inline-block; position: relative; width: 2.239em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-553\"><span class=\"mrow\" id=\"MathJax-Span-554\"><span class=\"mn\" id=\"MathJax-Span-555\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.15em, 4.243em, -999.998em); top: -3.959em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-564\"><span class=\"mrow\" id=\"MathJax-Span-565\"><span class=\"mi\" id=\"MathJax-Span-566\" style=\"font-family: MathJax_Math-italic;\">z<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-567\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-568\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-575\"><span class=\"mrow\" id=\"MathJax-Span-576\"><span class=\"mn\" id=\"MathJax-Span-577\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1002.24em, 6.247em, -999.998em); top: -4.564em; left: 6.526em;\"><span style=\"display: inline-block; position: relative; width: 2.286em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.336em, -999.998em); top: -5.356em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-556\"><span class=\"mrow\" id=\"MathJax-Span-557\"><span class=\"mn\" id=\"MathJax-Span-558\" style=\"font-family: MathJax_Main;\">5<\/span><span class=\"mo\" id=\"MathJax-Span-559\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mi\" id=\"MathJax-Span-560\" style=\"font-family: MathJax_Math-italic; padding-left: 0.235em;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-569\"><span class=\"mrow\" id=\"MathJax-Span-570\"><span class=\"mn\" id=\"MathJax-Span-571\" style=\"font-family: MathJax_Main;\">7<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-578\"><span class=\"mrow\" id=\"MathJax-Span-579\"><span class=\"mi\" id=\"MathJax-Span-580\" style=\"font-family: MathJax_Math-italic;\">a<\/span><span class=\"mo\" id=\"MathJax-Span-581\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-582\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-583\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-19\">\\left[\\begin{array}{ccc}  x-1 & 2 & 5-y \\\\  0 & z-1 & 7 \\\\  1 & 0 & a-5  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-20-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-584\" style=\"width: 6.014em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 5.175em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1004.85em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-585\"><span class=\"mrow\" id=\"MathJax-Span-586\"><span class=\"mo\" id=\"MathJax-Span-587\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-588\"><span style=\"display: inline-block; position: relative; width: 3.497em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-589\"><span class=\"mrow\" id=\"MathJax-Span-590\"><span class=\"mn\" id=\"MathJax-Span-591\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-598\"><span class=\"mrow\" id=\"MathJax-Span-599\"><span class=\"mn\" id=\"MathJax-Span-600\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-607\"><span class=\"mrow\" id=\"MathJax-Span-608\"><span class=\"mn\" id=\"MathJax-Span-609\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-592\"><span class=\"mrow\" id=\"MathJax-Span-593\"><span class=\"mn\" id=\"MathJax-Span-594\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-601\"><span class=\"mrow\" id=\"MathJax-Span-602\"><span class=\"mn\" id=\"MathJax-Span-603\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-610\"><span class=\"mrow\" id=\"MathJax-Span-611\"><span class=\"mn\" id=\"MathJax-Span-612\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-595\"><span class=\"mrow\" id=\"MathJax-Span-596\"><span class=\"mn\" id=\"MathJax-Span-597\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-604\"><span class=\"mrow\" id=\"MathJax-Span-605\"><span class=\"mn\" id=\"MathJax-Span-606\" style=\"font-family: MathJax_Main;\">7<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-613\"><span class=\"mrow\" id=\"MathJax-Span-614\"><span class=\"mn\" id=\"MathJax-Span-615\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-616\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-20\">\\left[\\begin{array}{lll}  1 & 2 & 3 \\\\  0 & 4 & 7 \\\\  1 & 0 & 0  \\end{array}\\right]<\/script> then find the values x, y, z and a.<br> Answer:<br> Given <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-21-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-617\" style=\"width: 12.164em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 10.487em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1010.16em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-618\"><span class=\"mrow\" id=\"MathJax-Span-619\"><span class=\"mo\" id=\"MathJax-Span-620\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-621\"><span style=\"display: inline-block; position: relative; width: 8.809em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1002.24em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 2.332em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -1.163em;\"><span class=\"mtd\" id=\"MathJax-Span-622\"><span class=\"mrow\" id=\"MathJax-Span-623\"><span class=\"mi\" id=\"MathJax-Span-624\" style=\"font-family: MathJax_Math-italic;\">x<\/span><span class=\"mo\" id=\"MathJax-Span-625\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-626\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-635\"><span class=\"mrow\" id=\"MathJax-Span-636\"><span class=\"mn\" id=\"MathJax-Span-637\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-646\"><span class=\"mrow\" id=\"MathJax-Span-647\"><span class=\"mn\" id=\"MathJax-Span-648\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1002.15em, 6.107em, -999.998em); top: -4.471em; left: 3.311em;\"><span style=\"display: inline-block; position: relative; width: 2.239em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-627\"><span class=\"mrow\" id=\"MathJax-Span-628\"><span class=\"mn\" id=\"MathJax-Span-629\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.15em, 4.243em, -999.998em); top: -3.959em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-638\"><span class=\"mrow\" id=\"MathJax-Span-639\"><span class=\"mi\" id=\"MathJax-Span-640\" style=\"font-family: MathJax_Math-italic;\">z<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-641\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-642\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-649\"><span class=\"mrow\" id=\"MathJax-Span-650\"><span class=\"mn\" id=\"MathJax-Span-651\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1002.24em, 6.247em, -999.998em); top: -4.564em; left: 6.526em;\"><span style=\"display: inline-block; position: relative; width: 2.286em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.336em, -999.998em); top: -5.356em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-630\"><span class=\"mrow\" id=\"MathJax-Span-631\"><span class=\"mn\" id=\"MathJax-Span-632\" style=\"font-family: MathJax_Main;\">5<\/span><span class=\"mo\" id=\"MathJax-Span-633\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mi\" id=\"MathJax-Span-634\" style=\"font-family: MathJax_Math-italic; padding-left: 0.235em;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.002em;\"><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-643\"><span class=\"mrow\" id=\"MathJax-Span-644\"><span class=\"mn\" id=\"MathJax-Span-645\" style=\"font-family: MathJax_Main;\">7<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1002.24em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -1.116em;\"><span class=\"mtd\" id=\"MathJax-Span-652\"><span class=\"mrow\" id=\"MathJax-Span-653\"><span class=\"mi\" id=\"MathJax-Span-654\" style=\"font-family: MathJax_Math-italic;\">a<\/span><span class=\"mo\" id=\"MathJax-Span-655\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-656\" style=\"font-family: MathJax_Main; padding-left: 0.235em;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-657\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-21\">\\left[\\begin{array}{ccc}  x-1 & 2 & 5-y \\\\  0 & z-1 & 7 \\\\  1 & 0 & a-5  \\end{array}\\right]<\/script> = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-22-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-658\" style=\"width: 6.014em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 5.175em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1004.85em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-659\"><span class=\"mrow\" id=\"MathJax-Span-660\"><span class=\"mo\" id=\"MathJax-Span-661\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-662\"><span style=\"display: inline-block; position: relative; width: 3.497em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-663\"><span class=\"mrow\" id=\"MathJax-Span-664\"><span class=\"mn\" id=\"MathJax-Span-665\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-672\"><span class=\"mrow\" id=\"MathJax-Span-673\"><span class=\"mn\" id=\"MathJax-Span-674\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-681\"><span class=\"mrow\" id=\"MathJax-Span-682\"><span class=\"mn\" id=\"MathJax-Span-683\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-666\"><span class=\"mrow\" id=\"MathJax-Span-667\"><span class=\"mn\" id=\"MathJax-Span-668\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-675\"><span class=\"mrow\" id=\"MathJax-Span-676\"><span class=\"mn\" id=\"MathJax-Span-677\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-684\"><span class=\"mrow\" id=\"MathJax-Span-685\"><span class=\"mn\" id=\"MathJax-Span-686\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-669\"><span class=\"mrow\" id=\"MathJax-Span-670\"><span class=\"mn\" id=\"MathJax-Span-671\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-678\"><span class=\"mrow\" id=\"MathJax-Span-679\"><span class=\"mn\" id=\"MathJax-Span-680\" style=\"font-family: MathJax_Main;\">7<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-687\"><span class=\"mrow\" id=\"MathJax-Span-688\"><span class=\"mn\" id=\"MathJax-Span-689\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-690\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-22\">\\left[\\begin{array}{lll}  1 & 2 & 3 \\\\  0 & 4 & 7 \\\\  1 & 0 & 0  \\end{array}\\right]<\/script><br> we have x \u2013 1 = 1, 5 \u2013 y = 3, z \u2013 1 = 4,<br> a \u2013 5 = 0<br> \u21d2 x = 2, y = 2, z = 5, a = 5<\/p>\n\n<h3>Question 2.<br> Find the trace of <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-23-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-691\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-692\"><span class=\"mrow\" id=\"MathJax-Span-693\"><span class=\"mo\" id=\"MathJax-Span-694\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-695\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-696\"><span class=\"mrow\" id=\"MathJax-Span-697\"><span class=\"mn\" id=\"MathJax-Span-698\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-706\"><span class=\"mrow\" id=\"MathJax-Span-707\"><span class=\"mn\" id=\"MathJax-Span-708\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-716\"><span class=\"mrow\" id=\"MathJax-Span-717\"><span class=\"mn\" id=\"MathJax-Span-718\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-699\"><span class=\"mrow\" id=\"MathJax-Span-700\"><span class=\"mn\" id=\"MathJax-Span-701\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-709\"><span class=\"mrow\" id=\"MathJax-Span-710\"><span class=\"mo\" id=\"MathJax-Span-711\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-712\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-719\"><span class=\"mrow\" id=\"MathJax-Span-720\"><span class=\"mn\" id=\"MathJax-Span-721\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.06em, -999.998em); top: -4.471em; left: 3.777em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-702\"><span class=\"mrow\" id=\"MathJax-Span-703\"><span class=\"mo\" id=\"MathJax-Span-704\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-705\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-713\"><span class=\"mrow\" id=\"MathJax-Span-714\"><span class=\"mn\" id=\"MathJax-Span-715\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-722\"><span class=\"mrow\" id=\"MathJax-Span-723\"><span class=\"mn\" id=\"MathJax-Span-724\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-725\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-23\">\\left[\\begin{array}{ccc}  1 & 3 & -5 \\\\  2 & -1 & 5 \\\\  1 & 0 & 1  \\end{array}\\right]<\/script><\/h3>\n\n<p>Answer:<br> Trace of the given matrix<br> = 1 \u2013 1 + 1 = sum of the diagonal elements<br> = 1<\/p>\n\n<h3>Question 3.<br> If A = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-24-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-726\" style=\"width: 6.945em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 5.967em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1005.64em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-727\"><span class=\"mrow\" id=\"MathJax-Span-728\"><span class=\"mo\" id=\"MathJax-Span-729\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-730\"><span style=\"display: inline-block; position: relative; width: 4.289em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.06em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-731\"><span class=\"mrow\" id=\"MathJax-Span-732\"><span class=\"mn\" id=\"MathJax-Span-733\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-740\"><span class=\"mrow\" id=\"MathJax-Span-741\"><span class=\"mn\" id=\"MathJax-Span-742\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-749\"><span class=\"mrow\" id=\"MathJax-Span-750\"><span class=\"mn\" id=\"MathJax-Span-751\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-734\"><span class=\"mrow\" id=\"MathJax-Span-735\"><span class=\"mn\" id=\"MathJax-Span-736\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-743\"><span class=\"mrow\" id=\"MathJax-Span-744\"><span class=\"mn\" id=\"MathJax-Span-745\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-752\"><span class=\"mrow\" id=\"MathJax-Span-753\"><span class=\"mn\" id=\"MathJax-Span-754\" style=\"font-family: MathJax_Main;\">5<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-737\"><span class=\"mrow\" id=\"MathJax-Span-738\"><span class=\"mn\" id=\"MathJax-Span-739\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.171em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-746\"><span class=\"mrow\" id=\"MathJax-Span-747\"><span class=\"mn\" id=\"MathJax-Span-748\" style=\"font-family: MathJax_Main;\">4<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-755\"><span class=\"mrow\" id=\"MathJax-Span-756\"><span class=\"mo\" id=\"MathJax-Span-757\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-758\" style=\"font-family: MathJax_Main;\">6<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-759\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-24\">\\left[\\begin{array}{ccc}  0 & 1 & 2 \\\\  2 & 3 & 4 \\\\  4 & 5 & -6  \\end{array}\\right]<\/script> and B = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-25-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-760\" style=\"width: 7.831em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 6.759em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(2.146em, 1006.43em, 6.2em, -999.998em); top: -4.425em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-761\"><span class=\"mrow\" id=\"MathJax-Span-762\"><span class=\"mo\" id=\"MathJax-Span-763\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a1<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a3<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a2<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-764\"><span style=\"display: inline-block; position: relative; width: 5.082em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.332em, 1001.21em, 6.107em, -999.998em); top: -4.471em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-765\"><span class=\"mrow\" id=\"MathJax-Span-766\"><span class=\"mo\" id=\"MathJax-Span-767\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-768\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-775\"><span class=\"mrow\" id=\"MathJax-Span-776\"><span class=\"mn\" id=\"MathJax-Span-777\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-784\"><span class=\"mrow\" id=\"MathJax-Span-785\"><span class=\"mn\" id=\"MathJax-Span-786\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.332em, 1000.47em, 6.107em, -999.998em); top: -4.471em; left: 2.286em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-769\"><span class=\"mrow\" id=\"MathJax-Span-770\"><span class=\"mn\" id=\"MathJax-Span-771\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-778\"><span class=\"mrow\" id=\"MathJax-Span-779\"><span class=\"mn\" id=\"MathJax-Span-780\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-787\"><span class=\"mrow\" id=\"MathJax-Span-788\"><span class=\"mn\" id=\"MathJax-Span-789\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.476em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.425em, 1001.21em, 6.247em, -999.998em); top: -4.564em; left: 3.777em;\"><span style=\"display: inline-block; position: relative; width: 1.26em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -5.356em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-772\"><span class=\"mrow\" id=\"MathJax-Span-773\"><span class=\"mn\" id=\"MathJax-Span-774\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.959em; left: 50%; margin-left: -0.231em;\"><span class=\"mtd\" id=\"MathJax-Span-781\"><span class=\"mrow\" id=\"MathJax-Span-782\"><span class=\"mn\" id=\"MathJax-Span-783\" style=\"font-family: MathJax_Main;\">0<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1001.21em, 4.243em, -999.998em); top: -2.561em; left: 50%; margin-left: -0.65em;\"><span class=\"mtd\" id=\"MathJax-Span-790\"><span class=\"mrow\" id=\"MathJax-Span-791\"><span class=\"mo\" id=\"MathJax-Span-792\" style=\"font-family: MathJax_Main;\">\u2212<\/span><span class=\"mn\" id=\"MathJax-Span-793\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.569em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-794\" style=\"vertical-align: 2.146em;\"><span style=\"display: inline-block; position: relative; width: 0.655em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Size4; top: -2.84em; left: 0em;\">\u23a4<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; font-family: MathJax_Size4; top: -0.836em; left: 0em;\">\u23a6<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"font-family: MathJax_Size4; position: absolute; top: -1.815em; left: 0em;\">\u23a5<span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.429em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.943em; border-left: 0px solid; width: 0px; height: 4.543em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-25\">\\left[\\begin{array}{ccc}  -1 & 2 & 3 \\\\  0 & 1 & 0 \\\\  0 & 0 & -1  \\end{array}\\right]<\/script> find A \u2013 B and 4A \u2013 5B.<\/h3>\n\n<p>Answer:<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5635\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-6.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-6\" width=\"317\" height=\"547\" sizes=\"auto, (max-width: 317px) 100vw, 317px\" data-pin-description=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-6\" data-pin-title=\"TS Inter 1st Year Maths 1A Solutions Chapter 3 Matrices Ex 3(a)\"><\/p>\n\n<h3>Question 4.<br> If A = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-26-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-795\" style=\"width: 5.734em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.942em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1004.71em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-796\"><span class=\"mrow\" id=\"MathJax-Span-797\"><span class=\"mo\" id=\"MathJax-Span-798\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-799\"><span style=\"display: inline-block; position: relative; width: 3.497em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.942em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-800\"><span class=\"mrow\" id=\"MathJax-Span-801\"><span class=\"mn\" id=\"MathJax-Span-802\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-809\"><span class=\"mrow\" id=\"MathJax-Span-810\"><span class=\"mn\" id=\"MathJax-Span-811\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-803\"><span class=\"mrow\" id=\"MathJax-Span-804\"><span class=\"mn\" id=\"MathJax-Span-805\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-812\"><span class=\"mrow\" id=\"MathJax-Span-813\"><span class=\"mn\" id=\"MathJax-Span-814\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-806\"><span class=\"mrow\" id=\"MathJax-Span-807\"><span class=\"mn\" id=\"MathJax-Span-808\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-815\"><span class=\"mrow\" id=\"MathJax-Span-816\"><span class=\"mn\" id=\"MathJax-Span-817\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-818\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-26\">\\left[\\begin{array}{lll}  1 & 2 & 3 \\\\  3 & 2 & 1  \\end{array}\\right]<\/script> and B = <span class=\"MathJax_Preview\" style=\"\"><\/span><span class=\"MathJax\" id=\"MathJax-Element-27-Frame\" tabindex=\"0\" style=\"\"><nobr><span class=\"math\" id=\"MathJax-Span-819\" style=\"width: 5.734em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.942em; height: 0px; font-size: 116%;\"><span style=\"position: absolute; clip: rect(1.773em, 1004.71em, 4.429em, -999.998em); top: -3.353em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-820\"><span class=\"mrow\" id=\"MathJax-Span-821\"><span class=\"mo\" id=\"MathJax-Span-822\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">[<\/span><\/span><span class=\"mtable\" id=\"MathJax-Span-823\"><span style=\"display: inline-block; position: relative; width: 3.497em; height: 0px; margin-right: 0.189em; margin-left: 0.189em;\"><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-824\"><span class=\"mrow\" id=\"MathJax-Span-825\"><span class=\"mn\" id=\"MathJax-Span-826\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-833\"><span class=\"mrow\" id=\"MathJax-Span-834\"><span class=\"mn\" id=\"MathJax-Span-835\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.895em, -999.998em); top: -4.005em; left: 1.493em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-827\"><span class=\"mrow\" id=\"MathJax-Span-828\"><span class=\"mn\" id=\"MathJax-Span-829\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-836\"><span class=\"mrow\" id=\"MathJax-Span-837\"><span class=\"mn\" id=\"MathJax-Span-838\" style=\"font-family: MathJax_Main;\">2<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(2.565em, 1000.47em, 4.942em, -999.998em); top: -4.005em; left: 2.985em;\"><span style=\"display: inline-block; position: relative; width: 0.515em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.218em, 1000.42em, 4.15em, -999.998em); top: -4.658em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-830\"><span class=\"mrow\" id=\"MathJax-Span-831\"><span class=\"mn\" id=\"MathJax-Span-832\" style=\"font-family: MathJax_Main;\">1<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><span style=\"position: absolute; clip: rect(3.218em, 1000.47em, 4.15em, -999.998em); top: -3.26em; left: 0em;\"><span class=\"mtd\" id=\"MathJax-Span-839\"><span class=\"mrow\" id=\"MathJax-Span-840\"><span class=\"mn\" id=\"MathJax-Span-841\" style=\"font-family: MathJax_Main;\">3<\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 4.01em;\"><\/span><\/span><\/span><\/span><span class=\"mo\" id=\"MathJax-Span-842\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">]<\/span><\/span><\/span><\/span><span style=\"display: inline-block; width: 0px; height: 3.357em;\"><\/span><\/span><\/span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.132em; border-left: 0px solid; width: 0px; height: 2.922em;\"><\/span><\/span><\/nobr><\/span><script type=\"math\/tex\" id=\"MathJax-Element-27\">\\left[\\begin{array}{lll}  3 & 2 & 1 \\\\  1 & 2 & 3  \\end{array}\\right]<\/script> find 3B \u2013 2A.<\/h3>\n\n<p>Answer:<br> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-5634\" src=\"https:\/\/cdn.manabadi.co.in\/2026-img\/Intet-Math\/TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-7.png\" alt=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-7\" width=\"250\" height=\"229\" data-pin-description=\"TS-Inter-1st-Year-Maths-1A-Solutions-Chapter-3-Matrices-Ex-3a-7\" data-pin-title=\"TS Inter 1st Year Maths 1A Solutions Chapter 3 Matrices Ex 3(a)\"><\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>TS Inter 1st Year Maths 1A Matrices Solutions Exercise 3(a) Question 1. Write the following as a single matrix. (i) [2 1 3] + [0 0 0] Answer: [2 1 3] + [0 0 0] = [2 + 0 1 + 0 3 + 0] = [2 1 3] (ii) \u23a1\u23a3\u23a201\u22121\u23a4\u23a6\u23a5+\u23a1\u23a3\u23a2\u2212110\u23a4\u23a6\u23a5 Answer: \u23a1\u23a3\u23a201\u22121\u23a4\u23a6\u23a5+\u23a1\u23a3\u23a2\u2212110\u23a4\u23a6\u23a5 = \u23a1\u23a3\u23a20\u221211+1\u22121+0\u23a4\u23a6\u23a5 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":2664,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1544,15,38],"tags":[1551,1550,1554,1549,1546,1552,1553,1559,1548,1265,1557,1545,1547,1556,1558,1555,1560],"class_list":["post-2623","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-study-material-tg-inter","category-telangana","category-tg-inter","tag-inter-1st-year-maths-1a-matrices-solutions","tag-intermediate-1st-year-maths-matrices-formulas-and-solutions","tag-intermediate-maths-1a-matrices-solved-examples","tag-maths-1a-chapter-3-important-questions","tag-maths-1a-chapter-3-matrices-ts-inter","tag-maths-1a-matrices-exercise-solutions","tag-maths-1a-matrices-step-by-step-solutions-ts-inter","tag-ts-inter-1st-year-maths-1a-chapter-3-matrices-solutions-pdf-download","tag-ts-inter-1st-year-maths-1a-matrices-pdf","tag-ts-inter-1st-year-maths-1a-solutions","tag-ts-inter-1st-year-maths-1a-textbook-solutions","tag-ts-inter-1st-year-matrices-solutions","tag-ts-inter-maths-1a-chapter-3-matrices","tag-ts-inter-maths-1a-chapter-3-matrices-solved-problems","tag-ts-inter-maths-1a-chapter-3-question-answers","tag-ts-inter-maths-1a-matrices-exam-preparation-material","tag-ts-intermediate-1st-year-maths-matrices"],"_links":{"self":[{"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/posts\/2623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/comments?post=2623"}],"version-history":[{"count":8,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/posts\/2623\/revisions"}],"predecessor-version":[{"id":2726,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/posts\/2623\/revisions\/2726"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/media\/2664"}],"wp:attachment":[{"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/media?parent=2623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/categories?post=2623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.manabadi.co.in\/boards\/wp-json\/wp\/v2\/tags?post=2623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}