{"id":1071,"date":"2021-12-17T16:30:20","date_gmt":"2021-12-17T11:00:20","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1071"},"modified":"2022-05-24T18:13:35","modified_gmt":"2022-05-24T12:43:35","slug":"study-materials-ncert-solutions-class-12-maths-chapter-3-matrices","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 3 Matrices"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#NCERT_Solutions_for_Class_12_Maths_Chapter_3_Matrices\" title=\"NCERT Solutions for Class 12 Maths Chapter 3 Matrices\">NCERT Solutions for Class 12 Maths Chapter 3 Matrices<\/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:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#The_NCERT_Solutions_to_questions_provided_by_Infinity_learn_has_covered_all_the_below-mentioned_properties_and_formulas\" title=\"The NCERT Solutions to questions provided by Infinity learn has covered all the below-mentioned properties and formulas.\">The NCERT Solutions to questions provided by Infinity learn has covered all the below-mentioned properties and formulas.<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#The_Frequently_Asked_Questions_about_NCERT_Solutions_in_this_chapter\" title=\"The Frequently Asked Questions about NCERT Solutions in this chapter.\">The Frequently Asked Questions about NCERT Solutions in this chapter.<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#What_are_the_main_topics_discussed_in_these_NCERT_Solutions\" title=\"What are the main topics discussed in these NCERT Solutions?\">What are the main topics discussed in these NCERT Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#Why_should_we_learn_about_matrices_from_NCERT_Solutions_in_this_chapter\" title=\"Why should we learn about matrices from NCERT Solutions in this chapter?\">Why should we learn about matrices from NCERT Solutions in this chapter?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/#Do_these_NCERT_Solutions_help_you_score_well_in_the_term_-_I_exam\" title=\"Do these NCERT Solutions help you score well in the term \u2013 I exam?\">Do these NCERT Solutions help you score well in the term \u2013 I exam?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Subject specialists have created NCERT solutions for class 12 maths chapter 3, including thorough solutions for reference. These\u202fsolutions are updated according to the latest term \u2013 I CBSE syllabus for 2021-22 and are provided in easy language for understanding. Tips and tricks are also provided.<\/p>\n<p>These solutions are provided so a student can clear his doubts and get help with a deep understanding of the concept. Also, you can refer them to make the chapter notes and revisions notes. You can also download PDF from the link.<\/p>\n<table data-tablestyle=\"MsoNormalTable\" data-tablelook=\"1184\" aria-rowcount=\"6\">\n<tbody>\n<tr aria-rowindex=\"2\">\n<td data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices-exercise-3-1\/\" target=\"_blank\" rel=\"noopener\">Exercise 3.1 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"3\">\n<td data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices-exercise-3-2\/\" target=\"_blank\" rel=\"noopener\">Exercise 3.2 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"4\">\n<td data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices-exercise-3-3\/\" target=\"_blank\" rel=\"noopener\">Exercise 3.3 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"5\">\n<td data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices-exercise-3-4\/\" target=\"_blank\" rel=\"noopener\">Exercise 3.4 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr aria-rowindex=\"6\">\n<td data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices-exercise-miscellaneous\/\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise on Chapter 3 Class 12<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b><span data-contrast=\"auto\">\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/1071\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-3.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-3.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Chapter 3<br\/><\/a><\/span><\/b><\/p>\n<h2 aria-level=\"3\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_3_Matrices\"><\/span><span style=\"font-size: 14pt;\"><b>NCERT Solutions for Class 12 Maths Chapter 3 Matrices<\/b><\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"auto\">These NCERT Solutions include the following topics and subtopics. Students should practice problems on these topics to get ready for the term \u2013 I exam with the help of Infinity Learn.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559740&quot;:240}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">3.1 Introduction<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">In this chapter, students learned the fundamentals of matrix and matrix algebra and how matrices are associated with different fields.<\/span><br \/>\n<b><\/b><\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.2 Matrix<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">3.2.1 Order of a matrix<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul style=\"list-style-type: circle;\">\n<li><span data-contrast=\"auto\">This portion clearly explains an easy example of how the elements are arranged to form a matrix and how its Order can be defined.<\/span><br \/>\n<b><\/b><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.3 Types of matrices<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">3.3.1 Equality of matrices<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul style=\"list-style-type: circle;\">\n<li><span data-contrast=\"auto\">We learned about different types of matrices in this section, such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices. Also, the equality of matrices is explained with examples.<\/span><br \/>\n<b><\/b><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.4 Operations on Matrices<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">3.4.1 Addition of matrices<\/span><\/li>\n<li><span data-contrast=\"auto\">3.4.2 Multiplication of a matrix by a scalar<\/span><\/li>\n<li><span data-contrast=\"auto\">3.4.3 Properties of matrix addition<\/span><\/li>\n<li><span data-contrast=\"auto\">3.4.4 Properties of scalar multiplication of a matrix<\/span><\/li>\n<li><span data-contrast=\"auto\">3.4.5 Multiplication of matrices<\/span><\/li>\n<li><span data-contrast=\"auto\">3.4.6 Properties of multiplication of matrices<\/span><\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.5 Transpose of a Matrix<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">3.5.1 Properties of the transpose of the matrices<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul style=\"list-style-type: circle;\">\n<li><span data-contrast=\"auto\">The transposition of a matrix and properties are well explained with examples. These examples also prove the properties of the transpose of a matrix.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.6 Symmetric and Skew Symmetric Matrices<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">In this part, students will understand the definitions of symmetric and skew-symmetric matrices and the related theorems and examples.<\/span><br \/>\n<b><\/b><\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.7 Elementary Operation (Transformation) of a Matrix<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">After going through this section, students will learn transformations on a matrix. There are six operations, i.e., transformations on a matrix. Three are due to columns, and three are due to rows, known as elementary operations or transformations.<\/span><br \/>\n<b><\/b><\/li>\n<\/ul>\n<p><b><span data-contrast=\"auto\">3.8 Invertible Matrices<\/span><\/b><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">3.8.1 Inverse of a matrix by elementary operations<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul style=\"list-style-type: circle;\">\n<li><span data-contrast=\"auto\">Here, students will understand the necessary conditions for matrices to have their inverse. Also, it has been given how to get an inverse matrix by performing elementary operations on the elements of a matrix.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"The_NCERT_Solutions_to_questions_provided_by_Infinity_learn_has_covered_all_the_below-mentioned_properties_and_formulas\"><\/span><span style=\"font-size: 12pt;\">The NCERT Solutions to questions provided by Infinity learn has covered all the below-mentioned properties and formulas.<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li><span data-contrast=\"auto\">An ordered rectangular array of numbers or functions is called a matrix.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A matrix with m rows and n columns is called a matrix of order m \u00d7 n.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">[aij]m\u00d71 is a column matrix.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">[aij]1\u00d7n is a row matrix.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">An m \u00d7 n matrix is a square matrix if m=n.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A = [aij]m\u00d7m is a diagonal matrix if aij=0, when i\u2260j.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A = [aij]n\u00d7n is a scalar matrix if aij=0, when i\u2260j, aij=k (k is some constant), when i=j.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A = [aij]n\u00d7n is an identity matrix if aij=1, when i=j, aij=0, when i\u2260j.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A zero matrix has all its elements as zero.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A = [aij] = [bij] = B if (i)A and B of the same order, (ii) aij = bij for all possible values of i and j.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">kA = k[aij]m\u00d7n = [k(aij)m\u00d7n]<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">-A = (-1) A<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A \u2013 B = A + (-1) B<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A + B = B + A<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">(A + B) + C = A + (B + C),\u202f where A, B and C are of the same order.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">k (A + B) = kA + kB, where A and B are of the same order, k is constant.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">(k + l) A = kA + lA, where k and l are constant.<\/span><span data-ccp-props=\"{&quot;134233117&quot;:true,&quot;134233118&quot;:true,&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:240}\"> <\/span><\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"The_Frequently_Asked_Questions_about_NCERT_Solutions_in_this_chapter\"><\/span><span style=\"font-size: 14pt;\">The Frequently Asked Questions about NCERT Solutions in this chapter.<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_are_the_main_topics_discussed_in_these_NCERT_Solutions\"><\/span>What are the main topics discussed in these NCERT Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn Mathematics, matrices are one of the easiest chapters; they are easy to understand. Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation on matrix, and invertible matrices are the main topics included in this chapter. These topics are discussed in easy language to help students score well in the first term exams irrespective of their intelligence quotient.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Why_should_we_learn_about_matrices_from_NCERT_Solutions_in_this_chapter\"><\/span>Why should we learn about matrices from NCERT Solutions in this chapter?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tMatrices represent rectangular arrays of numbers which are represented in rows and columns. Using matrices, various mathematical operations like multiplication, addition, subtraction, and division can be done. Representing the data related to infant mortality rate, population, etc., are the widely used areas where matrices are used to simplify the complex data. The other known use of matrices is statistics, plotting graphs, and various scientific research purposes. The method of solving difficult linear equations is also made easy using the matrices.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Do_these_NCERT_Solutions_help_you_score_well_in_the_term_-_I_exam\"><\/span>Do these NCERT Solutions help you score well in the term \u2013 I exam?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThis chapter includes all the important topics based on the latest update of CBSE guidelines. This chapter provides four exercises, giving the students numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams. These solutions are thus helpful to score well for the term 1 exam.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the main topics discussed in these NCERT Solutions?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In Mathematics, matrices are one of the easiest chapters; they are easy to understand. Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew-symmetric matrices, elementary operation on matrix, and invertible matrices are the main topics included in this chapter. These topics are discussed in easy language to help students score well in the first term exams irrespective of their intelligence quotient.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why should we learn about matrices from NCERT Solutions in this chapter?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Matrices represent rectangular arrays of numbers which are represented in rows and columns. Using matrices, various mathematical operations like multiplication, addition, subtraction, and division can be done. Representing the data related to infant mortality rate, population, etc., are the widely used areas where matrices are used to simplify the complex data. The other known use of matrices is statistics, plotting graphs, and various scientific research purposes. The method of solving difficult linear equations is also made easy using the matrices.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Do these NCERT Solutions help you score well in the term \u2013 I exam?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"This chapter includes all the important topics based on the latest update of CBSE guidelines. This chapter provides four exercises, giving the students numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams. These solutions are thus helpful to score well for the term 1 exam.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT solutions for class 12 maths chapter 3, including thorough solutions for reference. These\u202fsolutions are updated [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 12 Maths Chapter 3 Matrices","_yoast_wpseo_title":"NCERT Solutions Class 12 Maths Chapter 3 Matrices - Download Solution","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths Chapter 3 - Matrices solved by Expert Teachers as per NCERT (CBSE) Book guidelines at infinitylearn.com","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions Class 12 Maths Chapter 3 Matrices - Download Solution<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 12 Maths Chapter 3 - Matrices solved by Expert Teachers as per NCERT (CBSE) Book guidelines at infinitylearn.com\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-3-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 12 Maths Chapter 3 Matrices - 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