{"id":1074,"date":"2021-12-17T16:30:51","date_gmt":"2021-12-17T11:00:51","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1074"},"modified":"2023-04-27T12:44:08","modified_gmt":"2023-04-27T07:14:08","slug":"ncert-solutions-for-class-12-maths-chapter-4-determinantsstudy-materials-ncert-solutions-class-12-maths-chapter-4-determinants","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" 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\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#Maths_Class_12_NCERT_Solutions_Chapter_4_Exercises\" title=\"Maths Class 12 NCERT Solutions Chapter 4 Exercises \">Maths Class 12 NCERT Solutions Chapter 4 Exercises <\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#NCERT_Solutions_for_Class_12_Maths_Chapter_4_Determinants\" title=\"NCERT Solutions for Class 12 Maths Chapter 4 Determinants \">NCERT Solutions for Class 12 Maths Chapter 4 Determinants <\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#Key_Features_of_NCERT_Solutions_for_Class_12_Maths_Chapter_4_Determinants\" title=\"Key Features of NCERT Solutions for Class 12 Maths Chapter 4 Determinants\">Key Features of NCERT Solutions for Class 12 Maths Chapter 4 Determinants<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#Frequently_Asked_Questions_on_NCERT_Solutions_for_Class_12_Maths_Chapter_4\" title=\"Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 4\">Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 4<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#How_many_problems_are_there_in_NCERT_Solutions_for_Class_12_Maths_Chapter_4\" title=\"How many problems are there in NCERT Solutions for Class 12 Maths Chapter 4?\">How many problems are there in NCERT Solutions for Class 12 Maths Chapter 4?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#What_are_the_uses_of_determinants_according_to_NCERT_Solutions_for_Class_12_Maths_Chapter_4\" title=\"What are the uses of determinants according to NCERT Solutions for Class 12 Maths Chapter 4?\">What are the uses of determinants according to NCERT Solutions for Class 12 Maths Chapter 4?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#What_kind_of_problems_can_I_expect_in_the_first_term_exams_from_NCERT_Solutions_for_Class_12_Maths_Chapter_4\" title=\"What kind of problems can I expect in the first term exams from NCERT Solutions for Class 12 Maths Chapter 4?\">What kind of problems can I expect in the first term exams from NCERT Solutions for Class 12 Maths Chapter 4?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"auto\">Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 4 Determinants, including thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 12 provide useful solutions for improving conceptual knowledge.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in exams but also in helping Class 12 pupils perform well in upcoming competitive exams.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management is essential for getting the best results when answering questions.<\/span><\/p>\n<table style=\"width: 64.7416%; height: 216px;\" data-tablestyle=\"MsoNormalTable\" data-tablelook=\"1184\" aria-rowcount=\"8\">\n<tbody>\n<tr style=\"height: 48px;\" aria-rowindex=\"1\">\n<td style=\"height: 48px; width: 100%;\" data-celllook=\"69905\">\n<h3><span style=\"font-size: 12pt;\">Maths Class 12 NCERT Solutions Chapter 4 Exercises <\/span><\/h3>\n<\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"2\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-1\/\" target=\"_blank\" rel=\"noopener\">Exercise 4.1 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"3\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/\" target=\"_blank\" rel=\"noopener\">Exercise 4.2 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"4\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-3\/\" target=\"_blank\" rel=\"noopener\">Exercise 4.3 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"5\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-4\" target=\"_blank\" rel=\"noopener\">Exercise 4.4 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"6\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-5\" target=\"_blank\" rel=\"noopener\"><span data-contrast=\"auto\"><span style=\"color: #0000ff;\">Exercise 4.5 Class 12 Maths<\/span><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"7\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-6\" target=\"_blank\" rel=\"noopener\">Exercise 4.6 Class 12 Maths<\/a><\/span><\/td>\n<\/tr>\n<tr style=\"height: 24px;\" aria-rowindex=\"8\">\n<td style=\"height: 24px; width: 100%;\" data-celllook=\"69905\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-miscellaneous\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise on Chapter 4 Class 12<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? Are you preparing for Exams?<\/span>\n\t\t\t<span class=\"subtitle\">Study without Internet (Offline)<\/span>\n\t\t\t\n\t\t\t<button class=\"download-pdf-btn\" type=\"submit\"><img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/themes\/blog\/assets\/download-icon.svg\" alt=\"Download PDF icon\" width=\"18px\" height=\"18px\">Download PDF<\/button>\n\t\t<\/div>\n\t\t<div class=\"custom-model-main pdf-download-modal\">\n\t\t\t<div class=\"custom-model-inner\">\n\t\t\t\t<div class=\"close-modal-btn close-pdf-btn\">\u00d7<\/div>\n\t\t\t\t<div class=\"custom-model-wrap\">\n\t\t\t\t\t<div class=\"pop-up-content-wrap\">\n\t\t\t\t\t<div role=\"form\" class=\"wpcf7\" id=\"wpcf7-f314520-o1\" lang=\"en-US\" dir=\"ltr\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/surge\/wp-json\/wp\/v2\/posts\/1074#wpcf7-f314520-o1\" method=\"post\" class=\"wpcf7-form init\" novalidate=\"novalidate\" data-status=\"init\">\n<div style=\"display: none;\">\n<input type=\"hidden\" name=\"_wpcf7\" value=\"314520\" \/>\n<input type=\"hidden\" name=\"_wpcf7_version\" value=\"5.5.6\" \/>\n<input type=\"hidden\" name=\"_wpcf7_locale\" value=\"en_US\" \/>\n<input type=\"hidden\" name=\"_wpcf7_unit_tag\" value=\"wpcf7-f314520-o1\" \/>\n<input type=\"hidden\" name=\"_wpcf7_container_post\" value=\"0\" \/>\n<input type=\"hidden\" name=\"_wpcf7_posted_data_hash\" value=\"\" \/>\n<input type=\"hidden\" name=\"_wpcf7_recaptcha_response\" value=\"\" \/>\n<\/div>\n<div class=\"inline-form\">\n<p class=\"title\">Download PDF for Free.<br \/>\nStudy without Internet (Offline)<\/p>\n<p><span class=\"wpcf7-form-control-wrap your-first-name\"><input type=\"text\" name=\"your-first-name\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" id=\"user_name\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"First Name\" \/><\/span><\/p>\n<p><span class=\"wpcf7-form-control-wrap your-last-name\"><input type=\"text\" name=\"your-last-name\" value=\"\" size=\"40\" class=\"wpcf7-form-control wpcf7-text wpcf7-validates-as-required\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"Last Name\" \/><\/span><\/p>\n<p>  <label>Grade<\/label><br \/>\n  <span class=\"wpcf7-form-control-wrap your-grade\"><select name=\"your-grade\" class=\"wpcf7-form-control wpcf7-select wpcf7-validates-as-required grades-select\" aria-required=\"true\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"Class 1\">Class 1<\/option><option value=\"Class 2\">Class 2<\/option><option value=\"Class 3\">Class 3<\/option><option value=\"Class 4\">Class 4<\/option><option value=\"Class 5\">Class 5<\/option><option value=\"Class 6\">Class 6<\/option><option value=\"Class 7\">Class 7<\/option><option value=\"Class 8\">Class 8<\/option><option value=\"Class 9\">Class 9<\/option><option value=\"Class 10\">Class 10<\/option><option value=\"Class 11\">Class 11<\/option><option value=\"Class 12\">Class 12<\/option><\/select><\/span><\/p>\n<p>  <label>Target Exam<\/label><br \/>\n  <span class=\"wpcf7-form-control-wrap target-exam\"><select name=\"target-exam\" class=\"wpcf7-form-control wpcf7-select wpcf7-validates-as-required target-exam-select\" aria-required=\"true\" aria-invalid=\"false\"><option value=\"JEE\">JEE<\/option><option value=\"NEET\">NEET<\/option><option value=\"CBSE\">CBSE<\/option><\/select><\/span><\/p>\n<p style=\"display: flex;align-items: center;gap: 0.2rem;\">\n+91 <span class=\"wpcf7-form-control-wrap your-phone\"><input type=\"tel\" name=\"your-phone\" value=\"\" size=\"40\" maxlength=\"10\" minlength=\"10\" class=\"wpcf7-form-control wpcf7-text wpcf7-tel wpcf7-validates-as-required wpcf7-validates-as-tel\" id=\"otp_phone\" aria-required=\"true\" aria-invalid=\"false\" placeholder=\"Phone number\" \/><\/span>\n<\/p>\n<div id=\"otp_message\" class=\"otp_message\"><\/div>\n<p><label>Preferred time slot for the call<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap timeslot\"><select name=\"timeslot\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"9 am\">9 am<\/option><option value=\"10 am\">10 am<\/option><option value=\"11 am\">11 am<\/option><option value=\"12 pm\">12 pm<\/option><option value=\"1 pm\">1 pm<\/option><option value=\"2 pm\">2 pm<\/option><option value=\"3 pm\">3 pm<\/option><option value=\"4 pm\">4 pm<\/option><option value=\"5 pm\">5 pm<\/option><option value=\"6 pm\">6 pm<\/option><option value=\"7 pm\">7 pm<\/option><option value=\"8pm\">8pm<\/option><option value=\"9 pm\">9 pm<\/option><option value=\"10pm\">10pm<\/option><\/select><\/span><\/p>\n<p><label>Please indicate your interest<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap intent-checkbox\"><span class=\"wpcf7-form-control wpcf7-checkbox\"><span class=\"wpcf7-list-item first\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Live Classes\" \/><span class=\"wpcf7-list-item-label\">Live Classes<\/span><\/span><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Books\" \/><span class=\"wpcf7-list-item-label\">Books<\/span><\/span><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Test Series\" \/><span class=\"wpcf7-list-item-label\">Test Series<\/span><\/span><span class=\"wpcf7-list-item last\"><input type=\"checkbox\" name=\"intent-checkbox[]\" value=\"Self Learning\" \/><span class=\"wpcf7-list-item-label\">Self Learning<\/span><\/span><\/span><\/span><\/p>\n<p><label>Language<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap language\"><select name=\"language\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"English\">English<\/option><option value=\"Hindi\">Hindi<\/option><option value=\"Marathi\">Marathi<\/option><option value=\"Tamil\">Tamil<\/option><option value=\"Telugu\">Telugu<\/option><option value=\"Malayalam\">Malayalam<\/option><\/select><\/span><\/p>\n<p><label>Are you a Sri Chaitanya student?<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap sri-chaitanya-student\"><select name=\"sri-chaitanya-student\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"No\">No<\/option><option value=\"Yes\">Yes<\/option><\/select><\/span><\/p>\n<style>\n.intent-checkbox .wpcf7-checkbox{\n    display: flex;\n    flex-wrap: wrap;\n}\n.intent-checkbox .wpcf7-checkbox .wpcf7-list-item {\n    width: 50%;\n    margin: 0!important;\n    padding: 0.1rem;\n}\n<\/style>\n<p class=\"verify_otp_input\">Verify OTP Code (required)<br \/><span class=\"wpcf7-form-control-wrap phone_verify\"><input type=\"number\" name=\"phone_verify\" value=\"\" class=\"wpcf7-form-control wpcf7-number wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/1074\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-4.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Chapter-4.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Chapter 4<br\/><\/a>\n<h2><span style=\"font-size: 14pt;\"><b>NCERT Solutions for Class 12 Maths Chapter 4 Determinants<\/b> <\/span><\/h2>\n<p><span data-contrast=\"auto\">There are six exercises in Chapter Determinants, plus a miscellaneous exercise that includes all of the chapter&#8217;s questions. The following topics are covered in Chapter 4 NCERT Solutions for Class 12 Maths Term I:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.1 Introduction<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Students have already learned how to use matrices to represent a system of linear equations and use the determinant to determine whether or not this system has a unique solution. This section will be changed to include these items.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.2 Determinant<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul style=\"list-style-type: square;\">\n<li><b><span data-contrast=\"auto\">4.2.1<\/span><\/b><span data-contrast=\"auto\"> Determinant of a matrix of order one<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<li><b><span data-contrast=\"auto\">4.2.2<\/span><\/b><span data-contrast=\"auto\"> Determinant of a matrix of order two<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<li><b><span data-contrast=\"auto\">4.2.3<\/span><\/b><span data-contrast=\"auto\"> Determinant of a matrix of order 3 \u00d7 3<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">Students will learn how to find the determinant of a square matrix of various orders, such as one, two, and three, as well as examples, in this section.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.3 Properties of Determinants<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Students learned how to expand the determinants in the previous part. This section will look at certain determinant qualities that make evaluating them easier by determining the greatest number of zeros in a row or column. These principles hold for any order of determinants. However, it has only been applied to determinants of order three in this chapter.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.4 Area of a Triangle<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">When the coordinates of three vertices are supplied, we may use the formula to get the area of a triangle. You&#8217;ll learn how to find the area of a triangle by translating the points into a determinant in this section.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.5 Minors and Cofactors<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">After working through the problems in this part, students will be able to write the expansion of a determinant in compact form using minors and cofactors.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.6 Adjoint and Inverse of a Matrix<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.6.1<\/span><\/b> <b><span data-contrast=\"auto\">Adjoint of a matrix<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">After working through the exercises in this section, you&#8217;ll have a firm grasp of using an adjoint to obtain the inverse of a matrix. This section contains several theorems and examples to help you improve your skills.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.7 Applications of Determinants and Matrices<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"auto\">4.7.1 Solution of a system of linear equations using the inverse of a matrix<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">In these NCERT Solutions, you will get a detailed explanation of how to use determinants and matrices to solve systems of linear equations in two or three variables and how to assess the system&#8217;s coherence.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul style=\"list-style-type: square;\">\n<li><span data-contrast=\"auto\">Exercise 4.1 Solutions<\/span><span data-contrast=\"none\">: 8 Questions (2 Long, 5 Short Answers, 1 MCQ)<\/span><\/li>\n<li><span data-contrast=\"none\">Exercise 4.2 Solutions: 16 Questions(7 Long, 7 Short, 2 MCQs)<\/span><\/li>\n<li><span data-contrast=\"none\">Exercise 4.3 Solutions: 5 Questions ( 4 Short Answers, 1 MCQ)<\/span><\/li>\n<li><span data-contrast=\"none\">Exercise 4.4 Solutions: 5 Questions (4 Long, 1 MCQ)<\/span><\/li>\n<li><span data-contrast=\"none\">Exercise 4.5 Solutions: 18 Questions (11 Long, 5 Short, 2 MCQs)<\/span><\/li>\n<li><span data-contrast=\"none\">Exercise 4.6 Solutions: 16 Questions (13 Long, 3 Short)<\/span><\/li>\n<li><span data-contrast=\"none\">Miscellaneous Exercise Solutions: 19 Questions (15 Long, 1 Short, 3 MCQs)<\/span><\/li>\n<\/ul>\n<h3 aria-level=\"3\"><span class=\"ez-toc-section\" id=\"Key_Features_of_NCERT_Solutions_for_Class_12_Maths_Chapter_4_Determinants\"><\/span><span style=\"font-size: 12pt;\">Key Features of NCERT Solutions for Class 12 Maths Chapter 4 Determinants<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span data-contrast=\"auto\">The <\/span><b><span data-contrast=\"auto\">NCERT Solutions Class 12<\/span><\/b><span data-contrast=\"auto\"> of Infinity learn for Chapter 4 covers the following points and formulas. <\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"auto\">The value of the determinant is zero if any two rows or columns are identical or proportionate.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A square matrix. If and only if A is non-singular, it has an inverse.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">Unique solution of equation AX = B is given by X = A\u20131 B, where A \u2260 0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">A system of equations has a solution if it is consistent.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">There is no solution if a system of equations is inconsistent.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">For a square matrix A in matrix equation AX = B:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559739&quot;:240,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<ol>\n<li><span data-contrast=\"auto\">If | A| \u2260 0, then there exists a unique solution<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">If | A| = 0 and (adj A) B \u2260 0, then there exists no solution<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">If | A| = 0 and (adj A) B = 0, then system may or may not be consistent<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/li>\n<\/ol>\n<h4 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions_on_NCERT_Solutions_for_Class_12_Maths_Chapter_4\"><\/span><span style=\"font-size: 12pt;\">Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 4<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"How_many_problems_are_there_in_NCERT_Solutions_for_Class_12_Maths_Chapter_4\"><\/span>How many problems are there in NCERT Solutions for Class 12 Maths Chapter 4?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tExercise 4.1 has 8 questions, Exercise 4.2 has 16 questions, Exercises 4.3 and 4.4 have 5 questions, Exercise 4.5 has 18 questions, Exercise 4.6 has 16 questions, and the miscellaneous exercise has 19 questions. Long answers, short answers, and MCQs are included in each assignment, and they cover the areas that are important for the first term test. A team of Infinity Learn professionals with broad conceptual understanding creates the solutions for the exercise-specific issues.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_are_the_uses_of_determinants_according_to_NCERT_Solutions_for_Class_12_Maths_Chapter_4\"><\/span>What are the uses of determinants according to NCERT Solutions for Class 12 Maths Chapter 4?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tDeterminants are a key subject in algebra that has a variety of applications. This notion can be applied to the solution of a collection of linear equations. Students will understand the change in the area, volume, and variables in terms of integrals using determinants. It can also be used to calculate square matrices' values.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_kind_of_problems_can_I_expect_in_the_first_term_exams_from_NCERT_Solutions_for_Class_12_Maths_Chapter_4\"><\/span>What kind of problems can I expect in the first term exams from NCERT Solutions for Class 12 Maths Chapter 4?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThis chapter will cover issues using determinants to solve a set of linear equations. Proofs derived using determinant theory show that sums are also essential from the perspective of the term \u2013 I exam. It would help if you used determinants and their resulting values to determine the values of unknown variables in some instances.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How many problems are there in NCERT Solutions for Class 12 Maths Chapter 4?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Exercise 4.1 has 8 questions, Exercise 4.2 has 16 questions, Exercises 4.3 and 4.4 have 5 questions, Exercise 4.5 has 18 questions, Exercise 4.6 has 16 questions, and the miscellaneous exercise has 19 questions. Long answers, short answers, and MCQs are included in each assignment, and they cover the areas that are important for the first term test. A team of Infinity Learn professionals with broad conceptual understanding creates the solutions for the exercise-specific issues.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the uses of determinants according to NCERT Solutions for Class 12 Maths Chapter 4?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Determinants are a key subject in algebra that has a variety of applications. This notion can be applied to the solution of a collection of linear equations. Students will understand the change in the area, volume, and variables in terms of integrals using determinants. It can also be used to calculate square matrices' values.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What kind of problems can I expect in the first term exams from NCERT Solutions for Class 12 Maths Chapter 4?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"This chapter will cover issues using determinants to solve a set of linear equations. Proofs derived using determinant theory show that sums are also essential from the perspective of the term \u2013 I exam. It would help if you used determinants and their resulting values to determine the values of unknown variables in some instances.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 4 Determinants, including thorough solutions for reference. All of [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 12 Maths Chapter 4","_yoast_wpseo_title":"Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-12-17T11:00:51+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-04-27T07:14:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasad Gupta\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants","description":"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/","og_locale":"en_US","og_type":"article","og_title":"Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants","og_description":"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","og_url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2021-12-17T11:00:51+00:00","article_modified_time":"2023-04-27T07:14:08+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Prasad Gupta","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/","name":"Download NCERT Solutions for Class 12th Maths Chapter 4 Determinants","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2021-12-17T11:00:51+00:00","dateModified":"2023-04-27T07:14:08+00:00","description":"NCERT Solutions for Class 12 Maths Chapter 4 - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants","datePublished":"2021-12-17T11:00:51+00:00","dateModified":"2023-04-27T07:14:08+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants\/#webpage"},"wordCount":976,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["NCERT Solutions","NCERT Solutions For Class 12 Mathematics"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05","name":"Prasad Gupta","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","caption":"Prasad Gupta"},"url":"https:\/\/infinitylearn.com\/surge\/author\/prasad\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/1074"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=1074"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/1074\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=1074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=1074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=1074"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=1074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}