{"id":4481,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/"},"modified":"2018-05-08T09:47:29","modified_gmt":"2018-05-08T04:17:29","slug":"ncert-solutions-class-12-maths-exercise-3-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 3.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Matrices\" >NCERT Solutions class 12 Maths Matrices\u00a0<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#2_If_a_matrix_has_24_elements_what_are_possible_orders_it_can_order_What_if_it_has_13_elements\" >2. If a matrix has 24 elements, what are possible orders it can order? What, if it has 13 elements?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#3_If_a_matrix_has_18_elements_what_are_the_possible_orders_it_can_have_What_if_has_5_elements\" >3. If a matrix has 18 elements, what are the possible orders it can have? What if has 5 elements?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-2\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#4_Construct_a_2_x_2_matrix_A_whose_elements_are_given_by\" >4. Construct a 2 x 2 matrix A = \u00a0whose elements are given by:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-3\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#5_Construct_a_3_x_4_matrix_whose_elements_are_given_by\" >5. Construct a 3 x 4 matrix, whose elements are given by:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-4\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#6_Find_the_values_of_and_from_the_following_equations\" >6. Find the values of \u00a0and \u00a0from the following equations:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-5\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#7_Find_the_values_of_and_from_the_equation\" >7. Find the values of \u00a0and \u00a0from the equation .<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#8_A_is_a_square_matrix_if\" >8. A = \u00a0is a square matrix if:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-6\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#9_Which_of_the_given_values_of_and_make_the_following_pairs_of_matrices_equal\" >9. Which of the given values of \u00a0and \u00a0make the following pairs of matrices equal:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-7\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#10_The_number_of_all_possible_matrices_of_order_3_x_3_with_each_entry_0_or_1_is\" >10. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#NCERT_Solutions_class_12_Maths_Exercise_31-8\" >NCERT Solutions class 12 Maths Exercise 3.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 3.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-matrices\/1287\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Matrices\u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20pic.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 3.1\" width=\"180\" height=\"234\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Matrices\"><\/span>NCERT Solutions class 12 Maths Matrices<strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>1. In the matrix A = <img decoding=\"async\" style=\"height: 88px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image001.png\" \/>, write:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) The order of the matrix.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) The number of elements.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Write the elements <img decoding=\"async\" style=\"height: 24px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image002.png\" \/><\/strong><\/p>\n<p><strong>Ans. (i)<\/strong> There are 3 horizontal lines (rows) and 4 vertical lines (columns) in the given matrix A.<\/p>\n<p>Therefore, Order of the matrix is 3 x 4.<\/p>\n<p><strong>(ii)<\/strong> The number of elements in the matrix A is 3 x 4 = 12.<\/p>\n<p><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 24px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image003.png\" \/>\u00a0Element in first row and third column = 19<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image004.png\" \/>\u00a0Element in second row and first column = 35<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image005.png\" \/>\u00a0Element in third row and third column = <img decoding=\"async\" style=\"height: 19px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image006.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image007.png\" \/>\u00a0Element in second row and fourth column = 12<\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image008.png\" \/>\u00a0Element in second row and third column = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image009.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_If_a_matrix_has_24_elements_what_are_possible_orders_it_can_order_What_if_it_has_13_elements\"><\/span><strong>2. If a matrix has 24 elements, what are possible orders it can order? What, if it has 13 elements?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Since, a matrix having <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image010.png\" \/>\u00a0element is of order <img decoding=\"async\" style=\"height: 15px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image011.png\" \/><\/p>\n<p><strong>(i)<\/strong> Therefore, there are 8 possible matrices having 24 elements of orders 1 x 24, 2 x 12, 3 x 8, 4 x 6, 24 x 1, 12 x 2, 8 x 3, 6 x 4.<\/p>\n<p><strong>(ii)<\/strong> Prime number 13 = 1 x 13 and 13 x 1<\/p>\n<p>Therefore, there are 2 possible matrices of order 1 x 13 (Row matrix) and 13 x 1 (Column matrix).<\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_If_a_matrix_has_18_elements_what_are_the_possible_orders_it_can_have_What_if_has_5_elements\"><\/span><strong>3. If a matrix has 18 elements, what are the possible orders it can have? What if has 5 elements?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Since, a matrix having <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image010.png\" \/>\u00a0element is of order <img decoding=\"async\" style=\"height: 15px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image011.png\" \/><\/p>\n<p>(i) Therefore, there are 6 possible matrices having 18 elements of orders 1 x 18, 2 x 9, 3 x 6, 18 x 1, 9 x 2, 6 x 3.<\/p>\n<p>(ii) Prime number 5 = 1 x 5 and 5 x 1<\/p>\n<p>Therefore, there are 2 possible matrices of order 1 x 5 (Row matrix) and 5 x 1 (Column matrix).<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-2\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Construct_a_2_x_2_matrix_A_whose_elements_are_given_by\"><\/span><strong>4. Construct a 2 x 2 matrix A = <img decoding=\"async\" style=\"height: 30px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image012.png\" \/>\u00a0whose elements are given by:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 49px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image013.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 44px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image014.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 49px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image015.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. (i) <\/strong>Given:\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image013.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image016.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image017.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image018.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image019.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image020.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image021.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image022.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image023.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0A<sub>2 x 2<\/sub> = <img decoding=\"async\" style=\"height: 66px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image025.png\" \/><\/p>\n<p><strong>(ii)<\/strong> Given: <img decoding=\"async\" style=\"height: 44px; width: 46px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image014.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image016.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image026.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image018.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 50px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image027.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image020.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image028.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image022.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image029.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0A<sub>2 x 2<\/sub> = <img decoding=\"async\" style=\"height: 59px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image030.png\" \/><\/p>\n<p><strong>(iii)<\/strong> Given:\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image015.png\" \/>\u2026\u2026\u2026.(i)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image016.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image031.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image018.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image032.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image020.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image023.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image022.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 49px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image033.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 A<sub>2 x 2<\/sub> = <img decoding=\"async\" style=\"height: 59px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image034.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-3\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Construct_a_3_x_4_matrix_whose_elements_are_given_by\"><\/span><strong>5. Construct a 3 x 4 matrix, whose elements are given by:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 41px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image035.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 25px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image036.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. (i) <\/strong>Given: <img decoding=\"async\" style=\"height: 41px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image035.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image016.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image037.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image018.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image038.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image039.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image040.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image041.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image042.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image020.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image043.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image022.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 220px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image044.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image045.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 220px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image046.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image047.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image048.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image049.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image050.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image051.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 223px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image052.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image053.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image054.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image055.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 41px; width: 222px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image056.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 A<sub>3 x 4<\/sub> = <img decoding=\"async\" style=\"height: 100px; width: 351px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image057.png\" \/><\/p>\n<p><strong>(ii)<\/strong> Given: <img decoding=\"async\" style=\"height: 25px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image036.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image016.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 86px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image058.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image018.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image059.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image039.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image060.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image041.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image061.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image020.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image062.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image022.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image063.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image045.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image064.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image047.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image065.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image049.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image066.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image051.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image067.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image053.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image068.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 21px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image055.png\" \/>\u00a0in eq. (i) <img decoding=\"async\" style=\"height: 24px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image069.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 A<sub>3 x 4<\/sub> = <img decoding=\"async\" style=\"height: 75px; width: 318px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image070.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-4\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_Find_the_values_of_and_from_the_following_equations\"><\/span><strong>6. Find the values of <img decoding=\"async\" style=\"height: 17px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image071.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 13px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image072.png\" \/>\u00a0from the following equations:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 49px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image073.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 49px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image074.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 75px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image075.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. (i)<\/strong>Given:\u00a0 <img decoding=\"async\" style=\"height: 49px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image073.png\" \/><\/p>\n<p>By definition of Equal matrices, <img decoding=\"async\" style=\"height: 21px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image076.png\" \/><\/p>\n<p><strong>(ii) <\/strong><img decoding=\"async\" style=\"height: 49px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image074.png\" \/><\/p>\n<p>Equating corresponding entries, <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image077.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image078.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image080.png\" \/><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image081.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 21px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image082.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image083.png\" \/>\u00a0[From eq. (i), <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image084.png\" \/>]\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image085.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image086.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image087.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image088.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image089.png\" \/><\/p>\n<p>Putting these values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image090.png\" \/>\u00a0in eq. (i), we have <img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image091.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image092.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image093.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong>\u00a0 Given:\u00a0 <img decoding=\"async\" style=\"height: 75px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image075.png\" \/><\/p>\n<p>Equating corresponding entries, <img decoding=\"async\" style=\"height: 21px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image094.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image095.png\" \/>\u00a0 \u2026\u2026\u2026. (ii)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image096.png\" \/>\u2026\u2026\u2026.(iii)<\/p>\n<p>Eq. (i) \u2013 Eq. (ii) = <img decoding=\"async\" style=\"height: 17px; width: 27px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image097.png\" \/>\u00a09 \u2013 5 = 4<\/p>\n<p>Eq. (i) \u2013 Eq. (iii) = <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image098.png\" \/>\u00a09 \u2013 7 = 2<\/p>\n<p>Putting values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image090.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image099.png\" \/>\u00a0in eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image100.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image101.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image102.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-5\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_Find_the_values_of_and_from_the_equation\"><\/span><strong>7. Find the values of <img decoding=\"async\" style=\"height: 21px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image103.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 19px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image104.png\" \/>\u00a0from the equation <img decoding=\"async\" style=\"height: 49px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image105.png\" \/>.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equating corresponding entries,<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image106.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image107.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image108.png\" \/>\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image109.png\" \/>\u00a0\u2026\u2026\u2026.(iv)<\/p>\n<p>Eq. (i) \u2013 Eq. (ii) = <img decoding=\"async\" style=\"height: 19px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image110.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image111.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image111.png\" \/>\u00a0in eq. (i),\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image112.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image113.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image114.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image111.png\" \/>\u00a0in eq. (iii), <img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image115.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image116.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image117.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image117.png\" \/>\u00a0in eq. (iv), <img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image118.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image119.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image120.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image024.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image121.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_A_is_a_square_matrix_if\"><\/span><strong>8. A = <img decoding=\"async\" style=\"height: 31px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image122.png\" \/>\u00a0is a square matrix if:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 15px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image123.png\" \/>\u00a0(B) <img decoding=\"async\" style=\"height: 15px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image124.png\" \/>\u00a0(C) <img decoding=\"async\" style=\"height: 15px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image125.png\" \/>\u00a0(D) None of these<\/strong><\/p>\n<p><strong>Ans. <\/strong>By definition of square matrix <img decoding=\"async\" style=\"height: 15px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image125.png\" \/>, option (C) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-6\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Which_of_the_given_values_of_and_make_the_following_pairs_of_matrices_equal\"><\/span><strong>9. Which of the given values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image090.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image099.png\" \/>\u00a0make the following pairs of matrices equal:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" style=\"height: 49px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image126.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image127.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) Not possible to find <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image128.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image129.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Equating corresponding sides,<\/p>\n<p><img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image130.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 50px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image131.png\" \/><\/p>\n<p>And <img decoding=\"async\" style=\"height: 21px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image132.png\" \/><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image133.png\" \/><\/p>\n<p>Also <img decoding=\"async\" style=\"height: 21px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image134.png\" \/><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image133.png\" \/><\/p>\n<p>And <img decoding=\"async\" style=\"height: 19px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image135.png\" \/><img decoding=\"async\" style=\"height: 15px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image079.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image136.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since, values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image090.png\" \/>\u00a0are not equal, therefore, no values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image090.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image099.png\" \/>\u00a0exist to make the two matrices equal.<\/p>\n<p style=\"text-align: justify;\">Therefore, option (B) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-7\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_The_number_of_all_possible_matrices_of_order_3_x_3_with_each_entry_0_or_1_is\"><\/span><strong>10. The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>(A) 27<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) 18<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 81<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 512<\/strong><\/p>\n<p><strong>Ans. <\/strong>Since, general matrix of order 3 x 3 is <img decoding=\"async\" style=\"height: 75px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image137.png\" \/><\/p>\n<p>This matrix has 9 elements.<\/p>\n<p>The number of choices for <img decoding=\"async\" style=\"height: 24px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image138.png\" \/>\u00a0is 2 (as 0 or 1 can be used)<\/p>\n<p>Similarly, the number of choices for each other element is 2.<\/p>\n<p>Therefore, total possible arrangements (matrices) = <img decoding=\"async\" style=\"height: 19px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image139.png\" \/>\u00a0times = <img decoding=\"async\" style=\"height: 21px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex3.1\/image140.png\" \/><\/p>\n<p>Therefore, option (D) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_31-8\"><\/span>NCERT Solutions class 12 Maths Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Students\"><\/span>CBSE App for Students<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 3.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 3.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-3-1\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 3.1\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4481","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 3.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 3.1 in PDF format for free download. 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