{"id":1871,"date":"2021-12-23T12:00:56","date_gmt":"2021-12-23T06:30:56","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1871"},"modified":"2022-05-25T14:31:25","modified_gmt":"2022-05-25T09:01:25","slug":"study-materials-ncert-solutions-class-12-maths-chapter-4-determinants-exercise-4-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download"},"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'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/#Maths_NCERT_Solutions_Class_12_Chapter_4_-_Exercise_42\" title=\"Maths NCERT Solutions Class 12 Chapter 4 \u2013 Exercise 4.2\">Maths NCERT Solutions Class 12 Chapter 4 \u2013 Exercise 4.2<\/a><\/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-exercise-4-2\/#Determinant_Characteristics\" title=\"Determinant Characteristics\">Determinant Characteristics<\/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-exercise-4-2\/#Exercise_42_for_Class_12_Determinants\" title=\"Exercise 4.2 for Class 12 Determinants\">Exercise 4.2 for Class 12 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-exercise-4-2\/#FAQ\" title=\"FAQ:\">FAQ:<\/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-exercise-4-2\/#How_can_I_get_Infinity_Learns_Exercise_42_Class_12_Maths_NCERT_Solutions\" title=\"How can I get Infinity Learn&#039;s Exercise 4.2 Class 12 Maths NCERT Solutions?\">How can I get Infinity Learn&#039;s Exercise 4.2 Class 12 Maths NCERT Solutions?<\/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-exercise-4-2\/#According_to_Exercise_42_of_Chapter_4_of_Class_12_Maths_what_are_the_properties_of_determinants\" title=\"According to Exercise 4.2 of Chapter 4 of Class 12 Maths, what are the properties of determinants?\">According to Exercise 4.2 of Chapter 4 of Class 12 Maths, what are the properties of determinants?<\/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-exercise-4-2\/#When_you_say_a_determinant_is_zero_what_exactly_do_you_mean\" title=\"When you say a determinant is zero, what exactly do you mean?\">When you say a determinant is zero, what exactly do you mean?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><span data-contrast=\"none\">All Exercise 4.2 difficulties are answered in the NCERT Solutions for Class 12 Maths Chapter 4 Determinants. Subject specialists can easily master <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions<\/a><\/span>. Solving these difficulties could give kids the confidence to perform well on tests. Students can download the NCERT Class 12 Maths textbook and practice on their own to improve their grades.<\/span><\/p>\n<p aria-level=\"3\"><span data-contrast=\"none\">Access Answers to NCERT Class 12 Maths Chapter 4 Determinants Exercise 4.2 Page number 119<\/span><\/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\/1871#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\/1871\" 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\/Exercise-4.2.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\/Exercise-4.2.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\">Exercise 4.2<br\/><\/a>\n<h2 aria-level=\"2\"><span class=\"ez-toc-section\" id=\"Maths_NCERT_Solutions_Class_12_Chapter_4_-_Exercise_42\"><\/span><span style=\"color: #000000; font-size: 14pt;\">Maths NCERT Solutions Class 12 Chapter 4 \u2013 Exercise 4.2<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"none\">The <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions Class 12<\/a><\/span> Chapter 4 Exercise 4.2 Determinants will assist students in better understanding the types of problems frequently given in exams related to this topic. For a clear understanding of the ideas of Determinants, students should download and refer to Class 12 Maths Chapter 4 Exercise 4.2.<\/span><\/p>\n<p><span data-contrast=\"none\">These NCERT Solutions are available to all students who want to do well in their exams and get good grades. If you have problems while learning math or solving the questions in the Maths books&#8217; exercises, you can consult the Infinity Learn solutions for a full stepwise explanation of the sums. Download NCERT Solutions for Maths Class 12 Chapter 4 Exercise 4.2 Determinant to ensure a better learning experience.<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Determinant_Characteristics\"><\/span><span style=\"color: #000000; font-size: 14pt;\">Determinant Characteristics<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span data-contrast=\"none\">Students should be familiar with the properties of determinants to solve the amounts given in the ex 4.2 class 12 mathematics solutions. A determinant, as previously stated, is a specific integer that can be determined using a square matrix.<\/span><\/p>\n<p><span data-contrast=\"none\">A matrix&#8217;s determinant, commonly known as P, is indicated by det(P) or det P. Determinants are crucial features that allow an individual to get the same results with simpler and varied entry or element configurations.<\/span><\/p>\n<p><span data-contrast=\"none\">If students wish to get class 12 maths NCERT solutions, they should be aware of these features. We&#8217;ve compiled a list of those properties to assist students. That list can be found below.<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><b><span data-contrast=\"none\">Property of Reflection<\/span><\/b><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">According to this property, if the rows are transformed into columns, the determinant remains unchanged. The columns must also change into rows for this attribute to work.<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><b><span data-contrast=\"none\">All-Zero Property<\/span><\/b><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">It is a term used to describe a property that has no when all of the elements in a row or column are zero, the determinant&#8217;s value is also zero.<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><b><span data-contrast=\"none\">Proportionality or the Property of Repetition<\/span><\/b><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">This feature is critical for creating solutions to NCERT class 12 maths exercise 4.2. The value of the determinant is zero if all the components of a column or row are identical or proportional to the elements of another column or row, according to this property.<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><b><span data-contrast=\"none\">Changing Property<\/span><\/b><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">A change in the sign occurs when any two columns or rows of the determinant are swapped.<\/span><\/p>\n<ul>\n<li data-leveltext=\"\uf0b7\" data-font=\"Symbol\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"3\" data-aria-level=\"1\"><b><span data-contrast=\"none\">Multiple Scalar Properties<\/span><\/b><\/li>\n<\/ul>\n<p><span data-contrast=\"none\">When all the elements of a determinant&#8217;s column or row are multiplied by a non-zero constant, the determinant is multiplied by the same constants.<\/span><\/p>\n<p><span data-contrast=\"none\">Following are the topics covered in Class 12 Maths Chapter 4 Determinants Exercise 4.2:<\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"Roboto\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><span data-contrast=\"none\">Properties of Determinants<\/span><\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Exercise_42_for_Class_12_Determinants\"><\/span><span style=\"color: #000000;\">Exercise 4.2 for Class 12 Determinants<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span data-contrast=\"none\">For a student, 12th grade is a critical time. And if a student wants to make the most of that time, they should concentrate on achieving the best grades possible on the final exam. Students should complete all of the questions in Chapter 4, Exercise 4.2, to accomplish this goal in mathematics. But what if you require additional assistance? In that circumstance, Infinity Learn is always available to assist all pupils. Students may download NCERT solutions for class 12 maths from Infinity Learn. Infinity Learn provides these files for free to students.<\/span><\/p>\n<p><span data-contrast=\"none\">We also provide solutions for additional problems in the same chapter and <span style=\"color: #3366ff;\"><a style=\"color: #3366ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\" target=\"_blank\" rel=\"noopener\">NCERT solutions for class 12 maths<\/a><\/span> exercise 4.2. Exercises 4.1, 4.3, 4.4, 4.5, and 4.6 are all included in this chapter. Each of these exercises has approximately five questions.<\/span><\/p>\n<h4><span class=\"ez-toc-section\" id=\"FAQ\"><\/span><span style=\"color: #000000; font-size: 14pt;\">FAQ:<\/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_can_I_get_Infinity_Learns_Exercise_42_Class_12_Maths_NCERT_Solutions\"><\/span>How can I get Infinity Learn&#039;s Exercise 4.2 Class 12 Maths NCERT Solutions?<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\tDownloading solved maths questions from Infinity Learn is extremely straightforward. To begin, the learner should either download the Infinity Learn app or go to the Infinity Learn official website. Then proceed to register by providing a few of your details. Then, search for Exercise 4.2 Class 12 NCERT Solutions and click on the download link for the solved problems PDF. You may Learn the answers to the questions as soon as the file is finished downloading, so you can get the top grades in mathematics.\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=\"According_to_Exercise_42_of_Chapter_4_of_Class_12_Maths_what_are_the_properties_of_determinants\"><\/span>According to Exercise 4.2 of Chapter 4 of Class 12 Maths, what are the properties of determinants?<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\tThe ten main qualities of determinants are multiple scalar properties, switching property, sum property, reflection property, invariance property, factor property, triangle property, all-zero property, cofactor matrix property, and proportionality or repetition property. The exercise focuses on these features, and you must understand them well. Practice all determinant problems thoroughly, and if you have any questions, contact the Infinity Learn website.\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=\"When_you_say_a_determinant_is_zero_what_exactly_do_you_mean\"><\/span>When you say a determinant is zero, what exactly do you mean?<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\tWhen the determinant of a matrix is zero, the volume of the region defined by its columns or rows is zero, suggesting that the matrix, when used as a transformation, changes the basis vectors into linearly dependent vectors that define 0 volume. If any of the determinants is zero, the system has an infinite number of solutions. If two rows or columns are comparable, the determinant equals 0. If a matrix contains either a row of zeros or a column of zeros, its determinant equals 0.\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 can I get Infinity Learn's Exercise 4.2 Class 12 Maths NCERT Solutions?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Downloading solved maths questions from Infinity Learn is extremely straightforward. To begin, the learner should either download the Infinity Learn app or go to the Infinity Learn official website. Then proceed to register by providing a few of your details. Then, search for Exercise 4.2 Class 12 NCERT Solutions and click on the download link for the solved problems PDF. You may Learn the answers to the questions as soon as the file is finished downloading, so you can get the top grades in mathematics.\"\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\": \"According to Exercise 4.2 of Chapter 4 of Class 12 Maths, what are the properties of determinants?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The ten main qualities of determinants are multiple scalar properties, switching property, sum property, reflection property, invariance property, factor property, triangle property, all-zero property, cofactor matrix property, and proportionality or repetition property. The exercise focuses on these features, and you must understand them well. Practice all determinant problems thoroughly, and if you have any questions, contact the Infinity Learn website.\"\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\": \"When you say a determinant is zero, what exactly do you mean?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"When the determinant of a matrix is zero, the volume of the region defined by its columns or rows is zero, suggesting that the matrix, when used as a transformation, changes the basis vectors into linearly dependent vectors that define 0 volume. If any of the determinants is zero, the system has an infinite number of solutions. If two rows or columns are comparable, the determinant equals 0. If a matrix contains either a row of zeros or a column of zeros, its determinant equals 0.\"\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>All Exercise 4.2 difficulties are answered in the NCERT Solutions for Class 12 Maths Chapter 4 Determinants. Subject specialists can [&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":"Exercise 4.2 Class 12 Maths","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/"},"categories":[19,32,31],"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>NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - 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-exercise-4-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - 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-exercise-4-2\/\" \/>\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=\"2021-12-23T06:30:56+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-25T09:01:25+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":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download - Infinity Learn by Sri Chaitanya","description":"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - 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-exercise-4-2\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download - Infinity Learn by Sri Chaitanya","og_description":"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - 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-exercise-4-2\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2021-12-23T06:30:56+00:00","article_modified_time":"2022-05-25T09:01:25+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-exercise-4-2\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/","name":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2021-12-23T06:30:56+00:00","dateModified":"2022-05-25T09:01:25+00:00","description":"Free NCERT Solutions for Exercise 4.2 Class 12 Maths - 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-exercise-4-2\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/#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 Exercise 4.2 \u2013 CBSE Term I Free PDF Download"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.2 \u2013 CBSE Term I Free PDF Download","datePublished":"2021-12-23T06:30:56+00:00","dateModified":"2022-05-25T09:01:25+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-4-determinants-exercise-4-2\/#webpage"},"wordCount":898,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["NCERT Solutions","NCERT Solutions for Class 12","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\/1871"}],"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=1871"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/1871\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=1871"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=1871"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=1871"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=1871"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}