{"id":9293,"date":"2018-02-09T14:58:19","date_gmt":"2018-02-09T09:28:19","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9293"},"modified":"2019-03-02T15:44:32","modified_gmt":"2019-03-02T10:14:32","slug":"determinants-class-12-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/determinants-class-12-notes-mathematics\/","title":{"rendered":"Determinants class 12 Notes Mathematics"},"content":{"rendered":"<p><strong>Determinants class 12 Notes Mathematics<\/strong> in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Determinants 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 4 Determinants are also available for download in CBSE Guide website.<\/p>\n<h2>Determinants Class 12 Notes Mathematics<\/h2>\n<p>Download CBSE class 12th revision notes for chapter 4 Determinants in PDF format for free. Download revision notes for Determinants class 12 Notes and score high in exams. These are the Determinants class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 4 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>CBSE Class 12 Mathematics Chapter 4 Determinants<br \/>\n<\/strong><\/h2>\n<ul>\n<li>A determinant of a square matrix A is denoted by det.A or |A|.<\/li>\n<li>A determinant of order 1 x 1 matrix <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image001.png\" \/>is given by <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image002.png\" alt=\"Determinants Class 12 Notes Mathematics\" width=\"63\" height=\"24\" \/><\/li>\n<li>A determinant of order of 2 x 2 matrix A <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image003.png\" \/>is given by <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image004.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"231\" height=\"51\" \/><\/li>\n<li>A determinant of order 3 x 3 matrix A <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image005.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"82\" height=\"72\" \/>is given by (expanding along ( <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image006.png\" \/>) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image007.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"364\" height=\"75\" \/><\/li>\n<li>We can find the value ofa a determinant by expanding along any one of the three rows (or columns) and the value remains same.<\/li>\n<li>Generally, we find the value of a determinant by expanding along a row or column which has maximum number of zeroes.<\/li>\n<li><strong>For any square matrix A, the |A| satisfy following properties.<\/strong><\/li>\n<\/ul>\n<ol>\n<li>|A\u2032| = |A|, where A\u2032 = transpose of A.<\/li>\n<li>If we interchange any two rows (or columns), then sign of determinant changes.<\/li>\n<li>If any two rows or any two columns are identical or proportional, then value of determinant is zero.<\/li>\n<li>If we multiply each element of a row or a column of a determinant by constant k, then value of determinant is multiplied by k.<\/li>\n<li>Multiplying a determinant by k means multiply elements of only one row (or one column) by k.<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image008.png\" \/><\/li>\n<li>If elements of a row or a column in a determinant can be expressed as sum of two or more elements, then the given determinant can be expressed as sum of two or more determinants.<\/li>\n<li>If to each element of a row or a column of a determinant the equimultiples of corresponding elements of other rows or columns are added, then value of determinant remains same.<\/li>\n<\/ol>\n<ul>\n<li>If A is skew symmetric matrix of odd order, then |A| = 0.<\/li>\n<li>Area of a triangle with vertices <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image009.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"205\" height=\"27\" \/> is given by <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image010.png\" \/><\/li>\n<li><strong>Minors<\/strong>: Minor of an element a<sub>ij<\/sub> of the determinant of matrix A is the determinant obtained by deleting <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image011.png\" \/> row and <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image012.png\" \/>column and denoted by <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image013.png\" \/><\/li>\n<li><strong>Confactors<\/strong>: Cofactor of a<sub>ij<\/sub> of given by A<sub>ij<\/sub> = (\u2013 1)i+ j M<sub>ij<\/sub>.<\/li>\n<li>Value of determinant of a matrix A is obtained by sum of product of elements of a row (or a column) with corresponding cofactors. For example, <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image014.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"219\" height=\"24\" \/>.<\/li>\n<li>If elements of one row (or column) are multiplied with cofactors of elements of any other row (or column), then their sum is zero. For example, <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image015.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"214\" height=\"24\" \/><\/li>\n<li><strong>Adjoint of a matrix<\/strong>: <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image016.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"225\" height=\"27\" \/>where A is square matrix of order n.<\/li>\n<li><strong>Singular Matrix<\/strong>: A square matrix A is said to be singular or non-singular according as<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image017.png\" \/><\/li>\n<li><strong>Inverse of a square matrix<\/strong>: If AB = BA = I, where B is square matrix, then B is called inverse of A. Also <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image018.png\" \/><\/li>\n<li>A square matrix A has inverse if and only if A is non-singular.<\/li>\n<li><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image019.png\" \/><\/li>\n<li>If <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image020.png\" \/><\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image021.png\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image022.png\" \/><\/p>\n<p>then these equations can be written as AX = B, where<\/p>\n<p>\u2022 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image023.png\" alt=\"Determinants class 12 Notes Mathematics\" width=\"253\" height=\"75\" \/><\/p>\n<ul>\n<li>Unique solution of equation AX = B is given by <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image024.png\" \/><\/li>\n<li>A system of equation is consistent or inconsistent according as its solution exists or not.<\/li>\n<li>For a square matrix A in matrix equation AX = B<\/li>\n<\/ul>\n<p>\u2022 |<img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image025.png\" \/> there exists unique solution<\/p>\n<p>\u2022 |A| = 0 and (adj A) B \u2260 0, then there exists no solution<\/p>\n<p>\u2022 <img decoding=\"async\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/revise\/12\/mathematics\/ch04\/image026.png\" \/> then system may or may not be consistent and has infinite solutions.<strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong><\/p>\n<h2><strong>CBSE Class 12 Revision Notes and Key Points<\/strong><\/h2>\n<p>Determinants 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 Determinants 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 Determinants, NCERT Exemplar Determinants, 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\/matrices-class-12-notes-mathematics\/\">Matrices 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>Determinants class 12 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Determinants 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 4 Determinants are also available for &#8230; <a title=\"Determinants class 12 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/determinants-class-12-notes-mathematics\/\" aria-label=\"More on Determinants 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":[457,150,556,461,426,240],"class_list":["post-9293","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-determinants","tag-mathematics-notes","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>Determinants class 12 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Determinants class 12 Notes Mathematics chapter 4 in PDF format for free download. 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