{"id":9288,"date":"2018-02-09T14:48:39","date_gmt":"2018-02-09T09:18:39","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9288"},"modified":"2019-03-02T15:31:18","modified_gmt":"2019-03-02T10:01:18","slug":"matrices-class-12-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/matrices-class-12-notes-mathematics\/","title":{"rendered":"Matrices Class 12 Notes Mathematics"},"content":{"rendered":"<p><strong>Matrices Class 12 Notes Mathematics<\/strong> in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Matrices class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 3 Matrices are also available for download in CBSE Guide website.<\/p>\n<h2>Matrices Class 12 Notes Mathematics<\/h2>\n<p>Download CBSE class 12th revision notes for chapter 3 Matrices in PDF format for free. Download revision notes for Matrices class 12 Notes and score high in exams. These are the Matrices class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 3 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><\/strong><\/p>\n<h2><strong>CSBE Class 12 Mathematics Chapter 3 Matrices<\/strong><\/h2>\n<ul>\n<li>A <strong>matrix<\/strong> is an ordered rectangular array of numbers, real or complex\u00a0or functions.<\/li>\n<li>A matrix having m rows and n columns is called a matrix of <strong>order<\/strong> m \u00d7 n.<\/li>\n<li><strong>Column matrix<\/strong>: A matrix with one column is denoted by\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image001.png\" \/>.<\/li>\n<li><strong>Row matrix<\/strong>: A matrix with one row is denoted by\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image002.png\" \/>.<\/li>\n<li><strong>Square matrix<\/strong>:\u00a0An m \u00d7 n matrix is a square matrix if m = n.<\/li>\n<li><strong>Diagonal matrix<\/strong>:\u00a0A = <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image003.png\" \/>\u00a0is a diagonal matrix if\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image004.png\" \/>=0, when <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image005.png\" \/><\/li>\n<li><strong>Scalar matrix<\/strong>:\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image006.png\" \/>\u00a0is a scalar matrix if\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image007.png\" \/>\u00a0\u00a0when\u00a0 i \u2260\u00a0 j, \u00a0\u00a0<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image008.png\" \/>\u00a0\u00a0(k is <em>some constant), when I=j.<\/em><\/li>\n<li><strong>Identity matrix<\/strong>: <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image009.png\" \/>\u00a0is an identity matrix, if <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image010.png\" alt=\"Matrices class 12 Notes Mathematics\" width=\"280\" height=\"26\" \/><\/li>\n<li><strong>Zero matrix<\/strong>:\u00a0A zero matrix has all its elements as zero.<\/li>\n<li><strong>Equality of two matrices<\/strong>:\u00a0 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image011.png\" \/>\u00a0if (i) A and B are of same order, (ii) for all possible values of <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image012.png\" \/><\/li>\n<li><strong>Scalar multiplication<\/strong>:\u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image013.png\" alt=\"Matrices class 12 Notes Mathematics\" width=\"200\" height=\"34\" \/><\/li>\n<\/ul>\n<p>Also\u00a0\u00a0\u00a0 \u00a0\u00a0 \u2013 A = (\u20131)A<\/p>\n<ul>\n<li>A \u2013 B = A + (\u20131) B<\/li>\n<\/ul>\n<p>A + B = B + A<\/p>\n<p>(A + B) + C = A + (B + C), where A = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left[ {{a_{ij}}} \\right],\" \/><\/span><\/span>\u00a0B = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left[ {{b_{ij}}} \\right]\" \/><\/span><\/span>\u00a0and C = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left[ {{c_{ij}}} \\right]\" \/><\/span><\/span>\u00a0are of same order.<\/p>\n<ul>\n<li>k(A + B) = kA + kB, where A and B are of same order, k is constant.<\/li>\n<li>(k + l ) A = kA + lA, where k and l are constant.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image014.png\" alt=\"Matrices class 12 Notes Mathematics\" width=\"404\" height=\"26\" \/>where<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image015.png\" \/><\/p>\n<ul>\n<li>(i)\u00a0\u00a0\u00a0\u00a0 \u00a0A(BC) = (AB)C,<\/li>\n<\/ul>\n<p>(ii)\u00a0\u00a0\u00a0 \u00a0A(B + C) = AB + AC,<\/p>\n<p>(iii)\u00a0\u00a0\u00a0 (A + B)C = AC + BC<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image016.png\" alt=\"Matrices class 12 Notes Mathematics\" width=\"292\" height=\"31\" \/><\/li>\n<li>(i) (A\u2032)\u2032 = A, \u00b7\u00a0\u00a0 (ii) (kA)\u2032 = kA\u2032, \u00b7\u00a0\u00a0 (iii) (A + B)\u2032 = A\u2032 + B\u2032, \u00b7\u00a0\u00a0 (iv) (AB)\u2032 = B\u2032A\u2032<\/li>\n<li><strong>Symmetric matrix<\/strong>: A is a symmetric matrix if A\u2032 = A.<\/li>\n<li><strong>Skew-aymmetric matrix<\/strong>:\u00a0A is a skew symmetric matrix if A\u2032 = \u2013A.<\/li>\n<li>Any square matrix can be represented as the sum of a symmetric and a skew symmetric matrix. In fact, A = <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{1 \\over 2}\" \/><\/span><\/span>(A + A&#8217;) + <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{1 \\over 2}\" \/><\/span><\/span>(A &#8211; A&#8217;), where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{1 \\over 2}\" \/><\/span><\/span>(A + A&#8217;) is a symmetric matrix and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{1 \\over 2}\" \/><\/span><\/span>(A\u00a0&#8211; A&#8217;) is a skew-symmetric matrix.<\/li>\n<li><strong>Equivalent matrices<\/strong>:\u00a0Two matrices A and B are equivalent that is, A &#8211; B is A is obtained from the other by a sequence of elementary operations. Elementary operations of a matrix are as follows:<\/li>\n<\/ul>\n<p>(i)\u00a0\u00a0\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{R}}_i} \\leftrightarrow {{\\rm{R}}_j}\" \/><\/span><\/span>\u00a0or <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{C}}_i} \\to {{\\rm{C}}_j}\" \/><\/span><\/span>\u00a0(interchange rows or columns)<\/p>\n<p>(ii)\u00a0\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{R}}_i} \\to k{{\\rm{R}}_j}\" alt=\"Matrices class 12 Notes Mathematics\" width=\"71\" height=\"16\" \/><\/span><\/span>\u00a0or <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{C}}_i} \\to k{{\\rm{C}}_j}\" alt=\"Matrices class 12 Notes Mathematics\" width=\"70\" height=\"16\" \/><\/span><\/span><\/p>\n<p>(iii)\u00a0\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{R}}_i} \\to {{\\rm{R}}_i} + k{{\\rm{R}}_j}\" alt=\"Matrices class 12 Notes Mathematics\" width=\"109\" height=\"16\" \/><\/span><\/span>\u00a0or <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\rm{C}}_i} \\to {{\\rm{C}}_i} + k{{\\rm{C}}_j}\" alt=\"Matrices class 12 Notes Mathematics\" width=\"108\" height=\"16\" \/><\/span><\/span><\/p>\n<ul>\n<li>If A and B are two square matrices such that AB = BA = I, then B is the inverse matrix of A and is denoted by<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch03\/image020.png\" \/>\u00a0and A is the inverse of\u00a0 B.<\/li>\n<li>Inverse of a square matrix, if it exists, is unique.<strong>\u00a0 \u00a0 \u00a0\u00a0<\/strong><\/li>\n<\/ul>\n<h2><strong>CBSE Class 12 Revision Notes and Key Points<\/strong><\/h2>\n<p>Matrices class 12 Notes Mathematics. CBSE quick revision note for class-12 Chemistry Physics Math\u2019s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physics\/1251\/cbse-revision-notes\/7\/\">Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-chemistry\/1267\/cbse-revision-notes\/7\/\">Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics\/1284\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-biology\/1298\/cbse-revision-notes\/7\/\">Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-accountancy\/1315\/cbse-revision-notes\/7\/\">Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-economics\/1327\/cbse-revision-notes\/7\/\">Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-business-studies\/1727\/cbse-revision-notes\/7\/\">Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-computer-science\/1851\/cbse-revision-notes\/7\/\">Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-informatics-practices\/1873\/cbse-revision-notes\/7\/\">Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-english-core\/1855\/cbse-revision-notes\/7\/\">English Core<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-history\/1869\/cbse-revision-notes\/7\/\">History<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-12-physical-education\/1877\/cbse-revision-notes\/7\/\">Physical Education<\/a><\/li>\n<\/ul>\n<p>To download Matrices class 12 Notes Mathematics, sample paper 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 Matrices, NCERT Exemplar Matrices, 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<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/relations-functions-class-12-notes-mathematics\/\">Relations and Functions class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/inverse-trigonometric-functions-class-12-notes-mathematics\/\">Inverse Trigonometric Functions class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/determinants-class-12-notes-mathematics\/\">Determinants class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/continuity-differentiability-class-12-notes-mathematics\/\">Continuity and Differentiability class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/application-derivatives-class-12-notes-mathematics\/\">Application of Derivatives class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/integrals-class-12-notes-mathematics\/\">Integrals class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/application-integrals-class-12-notes-mathematics\/\">Application of Integrals class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/differential-equations-class-12-notes-mathematics\/\">Differential Equations class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/vector-algebra-class-12-notes-mathematics\/\">Vector Algebra class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/three-dimensional-geometry-class-12-notes-mathematics\/\">Three Dimensional Geometry class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-programming-class-12-notes-mathematics\/\">Linear Programming class 12 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-12-notes-mathematics\/\">Probability class 12 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Matrices Class 12 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Matrices class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 3 Matrices are also available for &#8230; <a title=\"Matrices Class 12 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/matrices-class-12-notes-mathematics\/\" aria-label=\"More on Matrices Class 12 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9266,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[48,456],"tags":[457,150,461,554,426,240],"class_list":["post-9288","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-12","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-mathematics-notes","tag-matrices","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matrices Class 12 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Matrices class 12 Notes Mathematics chapter 3 in PDF format for free download. 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