{"id":69017,"date":"2021-08-26T14:57:16","date_gmt":"2021-08-26T09:27:16","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69017"},"modified":"2021-08-26T19:37:08","modified_gmt":"2021-08-26T14:07:08","slug":"rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/","title":{"rendered":"RD Sharma Class 12 Solutions Chapter 6 Determinants Exercise 6.5 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-119928\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-6-Exercise-6.5.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-6-Exercise-6.5.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-6-Exercise-6.5-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5:\u00a0<\/strong>The RD Sharma textbook includes examples before each exercise to help students improve their problem-solving speed. These concepts are described in simple terms, allowing even non-math students to gain a better understanding of the subject. <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-12-solutions\/\"><strong>RD Sharma Class 12 Solutions<\/strong><\/a> are created by a team of experts with the goal of assisting students in their exam preparation. The key topic discussed in this exercise is the solution of a homogeneous system of linear equations. Students can use <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-6\/\"><strong>RD Sharma Solutions for Class 12 Maths Chapter 6<\/strong><\/a> Determinants Exercise 6.5 to help them succeed in their board exams.<\/p>\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-69d0ec44e53d6\" 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-69d0ec44e53d6\"><\/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\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#download-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65-free-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF<\/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\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-6-%e2%80%93-determinants-exercise-65-important-questions-with-solution\" title=\"Access answers to Maths RD Sharma Solutions For Class 12 Chapter 6 \u2013 Determinants Exercise 6.5 Important Questions With Solution\">Access answers to Maths RD Sharma Solutions For Class 12 Chapter 6 \u2013 Determinants Exercise 6.5 Important Questions With Solution<\/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\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#faqs-on-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65\" title=\"FAQs on RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5\">FAQs on RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5<\/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\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#what-are-the-advantages-of-using-rd-sharma-solutions-for-chapter-6-exercise-65-of-class-12-maths\" title=\"What are the advantages of using RD Sharma Solutions for Chapter 6 Exercise 6.5 of Class 12 Maths?\">What are the advantages of using RD Sharma Solutions for Chapter 6 Exercise 6.5 of Class 12 Maths?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#where-can-i-get-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65-free-pdf\" title=\"Where can I get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF?\">Where can I get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF?<\/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\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/#how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65\" title=\"How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5?\">How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65-free-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\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\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-6-Ex-6.5-1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Maths-Chapter-6-Ex-6.5-1.pdf\">RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-maths-rd-sharma-solutions-for-class-12-chapter-6-%e2%80%93-determinants-exercise-65-important-questions-with-solution\"><\/span>Access answers to Maths RD Sharma Solutions For Class 12 Chapter 6 \u2013 Determinants Exercise 6.5 Important Questions With Solution<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Solve each of the following system of homogeneous linear equations:<\/strong><\/p>\n<p><strong>1. x + y \u2013 2z = 0<\/strong><\/p>\n<p><strong>2x + y \u2013 3z =0<\/strong><\/p>\n<p><strong>5x + 4y \u2013 9z = 0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given x + y \u2013 2z = 0<\/p>\n<p>2x + y \u2013 3z =0<\/p>\n<p>5x + 4y \u2013 9z = 0<\/p>\n<p>Any system of equation can be written in matrix form as AX = B<\/p>\n<p>Now finding the Determinant of these set of equations,<\/p>\n<p><img class=\"alignnone size-full wp-image-119931\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/6.5.png\" alt=\"6.5\" width=\"320\" height=\"111\" \/><\/p>\n<p>= 1(1 \u00d7 (\u2013 9) \u2013 4 \u00d7 (\u2013 3)) \u2013 1(2 \u00d7 (\u2013 9) \u2013 5 \u00d7 (\u2013 3)) \u2013 2(4 \u00d7 2 \u2013 5 \u00d7 1)<\/p>\n<p>= 1(\u2013 9 + 12) \u2013 1(\u2013 18 + 15) \u2013 2(8 \u2013 5)<\/p>\n<p>= 1 \u00d7 3 \u20131 \u00d7 (\u2013 3) \u2013 2 \u00d7 3<\/p>\n<p>= 3 + 3 \u2013 6<\/p>\n<p>= 0<\/p>\n<p>Since D = 0, so the system of equation has infinite solution.<\/p>\n<p>Now let z = k<\/p>\n<p>\u21d2\u00a0x + y = 2k<\/p>\n<p>And 2x + y = 3k<\/p>\n<p>Now using the Cramer\u2019s rule<\/p>\n<p><img class=\"alignnone size-full wp-image-119932\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/6.5a.png\" alt=\"6.5a\" width=\"166\" height=\"470\" \/><\/p>\n<p><strong>2. 2x + 3y + 4z = 0<\/strong><\/p>\n<p><strong>x + y + z = 0<\/strong><\/p>\n<p><strong>2x + 5y \u2013 2z = 0<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img src=\"https:\/\/farm8.staticflickr.com\/7528\/16045411149_83ca031f13_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 6 Determinants Ex 6.5 Q2\" width=\"542\" height=\"265\" \/><br \/><strong>Chapter 6 Determinants Ex 6.5 Q3<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7516\/16045675947_084f88d45b_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 6 Determinants Ex 6.5 Q3\" width=\"254\" height=\"473\" \/><br \/><strong>Chapter 6 Determinants Ex 6.5 Q4<\/strong><br \/><img src=\"https:\/\/farm8.staticflickr.com\/7515\/16044019558_bec864ef60_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 6 Determinants Ex 6.5 Q4\" width=\"454\" height=\"436\" \/><br \/><strong>Chapter 6 Determinants Ex 6.5 Q5<\/strong><br \/><img src=\"https:\/\/farm9.staticflickr.com\/8612\/16231524545_2de4228cf6_o.png\" alt=\"RD Sharma Class 12 Solutions Chapter 6 Determinants Ex 6.5 Q5\" width=\"422\" height=\"225\" \/><\/p>\n<p>We have provided complete details of\u00a0<strong>RD Sharma Solutions Class 12 Maths Chapter 6<\/strong> Exercise 6.5. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 12 Exam, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65\"><\/span>FAQs on RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5<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-1629968048731\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-advantages-of-using-rd-sharma-solutions-for-chapter-6-exercise-65-of-class-12-maths\"><\/span>What are the advantages of using RD Sharma Solutions for Chapter 6 Exercise 6.5 of Class 12 Maths?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Referring to RD Sharma Solutions for Class 12 Maths Chapter 6 Exercise 6.5 will provide students a good understanding of the type of questions that might be asked in the Class 12 board exam from the chapter.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629968138116\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65-free-pdf\"><\/span>Where can I get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629968215008\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-12-maths-chapter-6-exercise-65\"><\/span>How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 5 questions in RD Sharma Solutions for Class 12 Maths Chapter 6 Exercise 6.5.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5:\u00a0The RD Sharma textbook includes examples before each exercise to help students improve their problem-solving speed. These concepts are described in simple terms, allowing even non-math students to gain a better understanding of the subject. RD Sharma Class 12 Solutions are created by a team of &#8230; <a title=\"RD Sharma Class 12 Solutions Chapter 6 Determinants Exercise 6.5 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-6-exercise-6-5\/\" aria-label=\"More on RD Sharma Class 12 Solutions Chapter 6 Determinants Exercise 6.5 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":119928,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3429,73223,73664,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69017"}],"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\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69017"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69017\/revisions"}],"predecessor-version":[{"id":119934,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69017\/revisions\/119934"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/119928"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}