{"id":91802,"date":"2021-05-28T13:02:00","date_gmt":"2021-05-28T07:32:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=91802"},"modified":"2021-05-28T13:25:20","modified_gmt":"2021-05-28T07:55:20","slug":"ncert-solutions-class-12-maths-chapter-3-exercise-3-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/","title":{"rendered":"NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3"},"content":{"rendered":"\n<p>NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3 includes all the Matrices questions of the Exercise. You can easily download the Free PDF for NCERT Solutions Maths Class 12.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-3-matrices\/\"><strong>NCERT Solutions Class 12 Maths Chapter 3: Matrices<\/strong><\/a><\/li>\n<\/ul>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 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\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d7b69d3416c\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" 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: #000000;color:#000000\" 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-69d7b69d3416c\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-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:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#download-free-pdf-for-ncert-solutions-class-12-maths-chapter-3-exercise-33\" title=\"Download Free PDF for NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3\">Download Free PDF for NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#topics-included-in-the-ncert-solutions-for-class-12-maths-exercise-33-pdf\" title=\"Topics included in the NCERT Solutions for Class 12 Maths Exercise 3.3 PDF\">Topics included in the NCERT Solutions for Class 12 Maths Exercise 3.3 PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#access-answers-other-ncert-class-12-chapter-3-matrices\" title=\"Access Answers other NCERT Class 12 Chapter 3 Matrices\u00a0\">Access Answers other NCERT Class 12 Chapter 3 Matrices\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#ncert-solutions-for-class-12-maths-exercise-33-matrices-formulas-used\" title=\"NCERT Solutions for Class 12 Maths Exercise 3.3- Matrices: Formulas Used\">NCERT Solutions for Class 12 Maths Exercise 3.3- Matrices: Formulas Used<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#faq-ncert-solutions-class-12-maths-chapter-3-exercise-33\" title=\"FAQ: NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3\">FAQ: NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#how-many-questions-are-included-in-the-ncert-solutions-class-12-maths-chapter-3-exercise-33\" title=\"How many questions are included in the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3?\">How many questions are included in the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#from-where-can-i-download-the-free-pdf-for-class-12-maths-chapter-3-exercise-33\" title=\"From where can I download the free PDF for Class 12 Maths Chapter 3 Exercise 3.3?\">From where can I download the free PDF for Class 12 Maths Chapter 3 Exercise 3.3?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#are-the-ncert-solutions-class-12-maths-ch-3-exercise-33-of-the-cbse-board\" title=\"Are the NCERT Solutions Class 12 Maths Ch 3 Exercise 3.3 of the CBSE Board? \">Are the NCERT Solutions Class 12 Maths Ch 3 Exercise 3.3 of the CBSE Board? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#what-are-the-important-topics-included-in-class-12-chapter-3-exercise-33-maths\" title=\"What are the important topics included in Class 12 Chapter 3 Exercise 3.3 Maths? \">What are the important topics included in Class 12 Chapter 3 Exercise 3.3 Maths? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#is-ncert-solutions-class-12-maths-matrix-an-easy-topic\" title=\"Is NCERT Solutions Class 12 Maths Matrix an easy topic? \">Is NCERT Solutions Class 12 Maths Matrix an easy topic? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#do-class-12-maths-books-are-same-for-pcm-and-commerce-students\" title=\"Do Class 12 Maths Books are same for PCM and Commerce students? \">Do Class 12 Maths Books are same for PCM and Commerce students? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/#are-ncert-solutions-class-12-maths-chapter-3-ex-33-useful-for-jee-exam\" title=\"Are NCERT Solutions Class 12 Maths Chapter 3 Ex 3.3 useful for JEE exam?\">Are NCERT Solutions Class 12 Maths Chapter 3 Ex 3.3 useful for JEE exam?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-free-pdf-for-ncert-solutions-class-12-maths-chapter-3-exercise-33\"><\/span>Download Free PDF for NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/05\/3.3.pdf\">Download NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3 <\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/05\/3.3.pdf\", \"#example1\");<\/script><\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p>You can easily download the PDF for Class 12 Maths Exercise 3.3 Chapter 3 that too absolutely free. This PDF is based on the all the important topics included in chapter 3 Exercise 3.3. The questions are based on the <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-12-board-exam\/\"><strong>12th CBSE board<\/strong><\/a> Maths Chapter 3 topics such as order, equality, transpose of a Matrix.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"topics-included-in-the-ncert-solutions-for-class-12-maths-exercise-33-pdf\"><\/span>Topics included in the NCERT Solutions for Class 12 Maths Exercise 3.3 PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>You can look over the topics included in NCERT Solutions Class 12 Maths Ch 3 Exercise 3.3<\/p>\n<ul>\n<li>Transpose of Matrix<\/li>\n<li>Properties of the transpose of the matrix<\/li>\n<li>Symmetric and skew-symmetric Matrices<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"access-answers-other-ncert-class-12-chapter-3-matrices\"><\/span>Access Answers other NCERT Class 12 Chapter 3 Matrices\u00a0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>You can also download the Free PDF for NCERT Solutions Class 12 Maths Chapter 3 other exercises:<\/p>\n<p>Class 12 Maths Chapter 3: Exercise 3.1<\/p>\n<p>Class 12 Maths Chapter 3: Exercise 3.2<\/p>\n<p>Class 12 Maths Chapter 3: Exercise 3.4<\/p>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-for-class-12-maths-exercise-33-matrices-formulas-used\"><\/span><strong>NCERT Solutions for Class 12 Maths Exercise 3.3- Matrices: Formulas Used<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Check out the basic formula used in NCERT Solutions Class 12 Maths Chapter 3 Exercises:<\/p>\n<ul>\n<li>A matrix that has m rows and n columns is called a matrix of order m \u00d7 n.<\/li>\n<li>[aij]m\u00d71 is a column matrix.<\/li>\n<li>[aij]1\u00d7n is a row matrix.<\/li>\n<li>An m \u00d7 n matrix is a square matrix if m=n.<\/li>\n<li>A = [aij]m\u00d7m is a diagonal matrix if aij=0, when i\u2260j.<\/li>\n<li>A = [aij]n\u00d7n is a scalar matrix if aij=0, when i\u2260j, aij=k (k is some constant), when i=j.<\/li>\n<li>A = [aij]n\u00d7n is an identity matrix if aij=1, when i=j, aij=0, when i\u2260j.<\/li>\n<li>A zero matrix has all its elements as zero.<\/li>\n<li>A = [aij] = [bij] = B if (i)A and B of the same order, (ii) aij = bij for all possible values of i and j.<\/li>\n<li>kA = k[aij]m\u00d7n = [k(aij)m\u00d7n]<\/li>\n<li>-A = (-1) A<\/li>\n<li>A \u2013 B = A + (-1) B<\/li>\n<li>A + B = B + A<\/li>\n<li>(A + B) + C = A + (B + C), where A, B and C are of the same order.<\/li>\n<li>k (A + B) = kA + kB, where A and B are of the same order, k is constant.<\/li>\n<li>(k + l) A = kA + lA, where k and l are constant.<\/li>\n<\/ul>\n<p>We have provided the NCERT Solutions PDF for Class 12 Maths Ch 3 Exercise 3.3. If you have any queries, feel free to ask in the comment section below.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-ncert-solutions-class-12-maths-chapter-3-exercise-33\"><\/span>FAQ: NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1622017047423\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-included-in-the-ncert-solutions-class-12-maths-chapter-3-exercise-33\"><\/span>How many questions are included in the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The total number of questions are included in the NCERT Solutions Class 12 Maths Ch 3 Exercise 3.3 are: 12 questions are further classified as 10 short questions and 2 multiple-choice questions.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017077107\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"from-where-can-i-download-the-free-pdf-for-class-12-maths-chapter-3-exercise-33\"><\/span>From where can I download the free PDF for Class 12 Maths Chapter 3 Exercise 3.3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can easily download the NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3 PDF from the above article that too absolutely free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017342795\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-the-ncert-solutions-class-12-maths-ch-3-exercise-33-of-the-cbse-board\"><\/span>Are the NCERT Solutions Class 12 Maths Ch 3 Exercise 3.3 of the CBSE Board? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, <strong><a aria-label=\"NCERT (opens in a new tab)\" href=\"https:\/\/ncert.nic.in\/\" target=\"_blank\" rel=\"noreferrer noopener\" class=\"rank-math-link\">NCERT<\/a> <\/strong>solutions for Class 12 Maths Chapter 3 Exercise 3.3 are of the CBSE board.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017367277\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-important-topics-included-in-class-12-chapter-3-exercise-33-maths\"><\/span>What are the important topics included in Class 12 Chapter 3 Exercise 3.3 Maths? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can look over the above article to get information regarding the topics included in Class 12 Maths Exercise 3.3.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017387746\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-ncert-solutions-class-12-maths-matrix-an-easy-topic\"><\/span>Is NCERT Solutions Class 12 Maths Matrix an easy topic? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, Matrix is one of the easiest topics in the Class 12 Maths.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017412135\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"do-class-12-maths-books-are-same-for-pcm-and-commerce-students\"><\/span>Do Class 12 Maths Books are same for PCM and Commerce students? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the syllabus for Class 12 Maths is the same for PCM and Commerce students.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622017435070\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"are-ncert-solutions-class-12-maths-chapter-3-ex-33-useful-for-jee-exam\"><\/span>Are NCERT Solutions Class 12 Maths Chapter 3 Ex 3.3 useful for JEE exam?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes you can easily prepare for JEE exam with the help of NCERT Solutions Class 12 Maths Chapter 3 Ex 3.3.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3 includes all the Matrices questions of the Exercise. You can easily download the Free PDF for NCERT Solutions Maths Class 12. NCERT Solutions Class 12 Maths Chapter 3: Matrices Download Free PDF for NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3 Download NCERT Solutions Class &#8230; <a title=\"NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-3-exercise-3-3\/\" aria-label=\"More on NCERT Solutions Class 12 Maths Chapter 3 Exercise 3.3\">Read more<\/a><\/p>\n","protected":false},"author":244,"featured_media":92490,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73413,2917,73693,73712,2985],"tags":[75409,75410,3570,75408,75043],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/91802"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=91802"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/91802\/revisions"}],"predecessor-version":[{"id":92505,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/91802\/revisions\/92505"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/92490"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=91802"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=91802"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=91802"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}