{"id":92218,"date":"2021-05-28T15:12:54","date_gmt":"2021-05-28T09:42:54","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=92218"},"modified":"2021-05-28T15:12:59","modified_gmt":"2021-05-28T09:42:59","slug":"ncert-solutions-class-12-maths-chapter-4-exercise-4-3","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/","title":{"rendered":"NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3"},"content":{"rendered":"\n<p><strong>NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3: <\/strong>NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3, comprises solutions of questions of Exercise 4.3. Subject experts have designed these NCERT Solutions for <a href=\"https:\/\/www.kopykitab.com\/Class-12-Maths\"><strong>Class 12 Maths<\/strong><\/a> easily and simply.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-for-class-12-maths-chapter-4-determinants\/\" target=\"_blank\" rel=\"noopener\"><strong>NCERT Solutions For Class 12 Maths Chapter 4: Determinants\u00a0<\/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-69d3cb4be2eee\" 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-69d3cb4be2eee\"><\/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-4-exercise-4-3\/#ncert-solutions-class-12-maths-chapter-4-exercise-43\" title=\"NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3\">NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<\/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:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#download-ncert-solutions-class-12-maths-chapter-4-exercise-43-pdf\" title=\"Download NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 PDF:\">Download NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 PDF:<\/a><\/li><\/ul><\/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-4-exercise-4-3\/#ncert-solutions-class-12-maths-chapter-4-exercise-43-2\" title=\"NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3\">NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#area-of-a-triangle\" title=\"Area of a triangle:\">Area of a triangle:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#why-study-from-ncert-solutions-class-12-maths-chapter-4-exercise-42\" title=\"Why study from NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.2?\">Why study from NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.2?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#access-other-exercise-ncert-solutions-of-class-12-maths-determinants\" title=\"Access Other Exercise NCERT Solutions of Class 12 Maths Determinants\">Access Other Exercise NCERT Solutions of Class 12 Maths Determinants<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#faqs-on-the-ncert-solutions-class-12-maths-chapter-4-exercise-43\" title=\"FAQs on the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3\">FAQs on the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<\/a><ul class='ez-toc-list-level-3'><li class='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-4-exercise-4-3\/#state-the-determinant-of-matrices-order-1\" title=\"State the Determinant of matrices order 1.\">State the Determinant of matrices order 1.<\/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-4-exercise-4-3\/#state-the-determinant-of-matrices-order-3-x-3\" title=\"State the Determinant of matrices order 3 x 3.\">State the Determinant of matrices order 3 x 3.<\/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-4-exercise-4-3\/#when-does-the-value-of-the-determinant-will-change-the-concerning-sign\" title=\"When does the value of the determinant will change the concerning sign?\">When does the value of the determinant will change the concerning sign?<\/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-4-exercise-4-3\/#what-happens-if-each-element-in-a-matrix-is-multiplied-by-a-constant-%e2%80%98k%e2%80%99\" title=\"What happens if each element in a matrix is multiplied by a constant, &#8216;k&#8217;?\">What happens if each element in a matrix is multiplied by a constant, &#8216;k&#8217;?<\/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-4-exercise-4-3\/#when-does-the-value-of-the-determinant-will-remain-unchanged\" title=\"When does the value of the determinant will remain unchanged?\">When does the value of the determinant will remain unchanged?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/#from-where-can-i-download-the-ncert-solutions-class-12-maths-chapter-4-exercise-43-free-pdf\" title=\"From where can I download the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 Free PDF?\">From where can I download the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 Free PDF?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-class-12-maths-chapter-4-exercise-43\"><\/span>NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/05\/4.3.pdf\" target=\"_blank\" rel=\"noopener\">NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 pdf<\/a><\/p>\n<p>\u00a0<\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<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\/4.3.pdf\", \"#example1\");<\/script><\/p>\n<h3><span class=\"ez-toc-section\" id=\"download-ncert-solutions-class-12-maths-chapter-4-exercise-43-pdf\"><\/span>Download NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 PDF:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: center;\"><a style=\"width: auto; padding: 18px; cursor: pointer; font-weight: bold; border-radius: 40px; color: #ffffff; background: #ff4500;\" href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/05\/4.3.pdf\" target=\"_blank\" rel=\"noopener\">Click Here<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"ncert-solutions-class-12-maths-chapter-4-exercise-43-2\"><\/span>NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 is giving an introduction to the term matrix and matrices so that you can understand the Determinants easily. It states that for every square matrix, you can assign a real number, known as a Determinant.\u00a0<\/p>\n<p>Determinant of matrices order 1:\u00a0<\/p>\n<p>If A = [a], matrix of order 1, Determinant of A is said to be equivalent of a.\u00a0<\/p>\n<p>Determinant of matrices order 2 x 2:<\/p>\n<p>In the case of Determinant of matrices order 2, Determinant is obtained by multiplying the matrices.\u00a0<\/p>\n<p>Determinant of matrices order 3 x 3:<\/p>\n<p>In the case of Determinant of matrices order 3 x 3, Determinant is obtained through a series of steps, explained in a detailed manner in the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3.\u00a0<\/p>\n<p>Here are some of the properties of the determinants, which you can also find in detail in the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3.\u00a0<\/p>\n<ul>\n<li>Property 1: The value of the determinant will remain unchanged when two rows or two columns are interchanged.\u00a0<\/li>\n<li>Property 2: The value of the determinant will change the concerning sign whenever two rows or two columns are interchanged.\u00a0<\/li>\n<li>Property 3: The value of the determinant will remain zero when two rows or two columns are the same.\u00a0<\/li>\n<li>Property 4: If each element in a matrix is multiplied by a constant, &#8216;k&#8217;, the value of the determinant will be multiplied by k, as well.\u00a0<\/li>\n<li>Property 5: If the sum of two terms is expressing elements, the value of the determinant will be expressed by the sum.\u00a0<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"area-of-a-triangle\"><\/span>Area of a triangle:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>You have studied this in earlier classes that the area of a triangle is equal to half into base into height. But here the area of a triangle is expressed like half of the value of matrix of order 3 x 3.\u00a0<\/p>\n<p>Some of the questions in exercise 4.3 are based on this concept and that&#8217;s why NCERT Solutions Class 12 Maths Chapter 4 has solved these questions in a detailed way.\u00a0<\/p>\n<h2><span class=\"ez-toc-section\" id=\"why-study-from-ncert-solutions-class-12-maths-chapter-4-exercise-42\"><\/span>Why study from NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.2?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>You might think if studying from NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.1 worth it? The answer is yes, and to support the claim, here are some good reasons.\u00a0<\/p>\n<ol>\n<li>High-quality content with reliable and accurate solutions.\u00a0<\/li>\n<li>Subject matter experts have designed the solutions.\u00a0<\/li>\n<li>All the answered are solved with steps and proper explanation, for your better understanding of concepts.<\/li>\n<li>The PDF form of the solutions is available which is easy to download and free of cost.\u00a0<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"access-other-exercise-ncert-solutions-of-class-12-maths-determinants\"><\/span>Access Other Exercise NCERT Solutions of Class 12 Maths Determinants<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>You can download the PDF of NCERT Solutions <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> Class 12 Maths for Chapter 4 other exercise:<\/p>\n<ul>\n<li><strong>Exercise 4.1<\/strong><\/li>\n<li><strong>Exercise 4.2<\/strong><\/li>\n<li><strong>Exercise 4.4<\/strong><\/li>\n<li><strong>Exercise 4.5<\/strong><\/li>\n<\/ul>\n<p><strong>All the best to the students appearing for the Class 12th board exam. Here is the detailed blog of NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3. For further queries regarding the Class 12th exam, you can ask in the comment box.\u00a0\u00a0<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-the-ncert-solutions-class-12-maths-chapter-4-exercise-43\"><\/span>FAQs on the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1622103032240\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"state-the-determinant-of-matrices-order-1\"><\/span>State the Determinant of matrices order 1.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Determinant of matrices order 1:\u00a0<br \/>If A = [a], matrix of order 1, Determinant of A is said to be equivalent of a.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622103045944\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"state-the-determinant-of-matrices-order-3-x-3\"><\/span>State the Determinant of matrices order 3 x 3.<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>In the case of Determinant of matrices order 3 x 3, Determinant is obtained through a series of steps.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622103075847\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"when-does-the-value-of-the-determinant-will-change-the-concerning-sign\"><\/span>When does the value of the determinant will change the concerning sign?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The value of the determinant will change the concerning sign whenever two rows or two columns are interchanged.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622103110748\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-happens-if-each-element-in-a-matrix-is-multiplied-by-a-constant-%e2%80%98k%e2%80%99\"><\/span>What happens if each element in a matrix is multiplied by a constant, &#8216;k&#8217;?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>If each element in a matrix is multiplied by a constant, &#8216;k&#8217;, the value of the determinant will be multiplied by k, as well.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622103146153\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"when-does-the-value-of-the-determinant-will-remain-unchanged\"><\/span>When does the value of the determinant will remain unchanged?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The value of the determinant will remain unchanged when two rows or two columns are interchanged.\u00a0<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1622103172152\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"from-where-can-i-download-the-ncert-solutions-class-12-maths-chapter-4-exercise-43-free-pdf\"><\/span>From where can I download the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download it from Kopykitab.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3: NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3, comprises solutions of questions of Exercise 4.3. Subject experts have designed these NCERT Solutions for Class 12 Maths easily and simply. NCERT Solutions For Class 12 Maths Chapter 4: Determinants\u00a0 NCERT Solutions Class 12 Maths Chapter 4 &#8230; <a title=\"NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/ncert-solutions-class-12-maths-chapter-4-exercise-4-3\/\" aria-label=\"More on NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.3\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":92567,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73413,2917,73693],"tags":[3429,3570,75043],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/92218"}],"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\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=92218"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/92218\/revisions"}],"predecessor-version":[{"id":92565,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/92218\/revisions\/92565"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/92567"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=92218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=92218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=92218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}