{"id":15546,"date":"2022-08-18T09:21:08","date_gmt":"2022-08-18T01:21:08","guid":{"rendered":"https:\/\/ocw.nycu.edu.tw\/?post_type=course_page&#038;p=15546"},"modified":"2026-06-08T16:39:50","modified_gmt":"2026-06-08T08:39:50","slug":"4-2-determinants-of-order-w","status":"publish","type":"course_page","link":"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-science\/department-of-applied-mathematics\/linear-algebra-i-department-of-applied-mathematics-prof-jonq-juang\/4-2-determinants-of-order-w","title":{"rendered":"4.2 Determinants of Order w"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"15546\" class=\"elementor elementor-15546\">\n\t\t\t\t\t\t\t\t\t<section class=\"penci-section penci-disSticky penci-structure-10 elementor-section elementor-top-section elementor-element elementor-element-3bba7640 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3bba7640\" 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100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-261e13d1 elementor-widget elementor-widget-shortcode\" data-id=\"261e13d1\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">\n<table id=\"tablepress-29\" class=\"tablepress tablepress-id-29\">\n<thead>\n<tr class=\"row-1 odd\">\n\t<th class=\"column-1\">Week<\/th><th class=\"column-2\">Course Content<\/th><th class=\"column-3\">Course Video<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e00\u7ae0 Vector Space<br \/>\n1.1 Introduction<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15438&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-3 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.2 Vector Space<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15456&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-4 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.3 Subspaces(\u5b50\u7a7a\u9593)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15463&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-5 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.4 Linear Combinations and Systems of Linear Equations<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15468&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-6 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.5 Linear Dependence and Linear Independence<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15474&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-7 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">1.6 Bases and Dimension (\u57fa\u5e95\u548c\u7dad\u5ea6)<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15480&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-8 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e8c\u7ae0 Linear Transformations and Matrices<br \/>\n2.1 Linear Transformations, Null spaces, and ranges<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15486&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-9 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.2 The Matrix Representation of a Linear Transformation<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15492&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-10 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.3 Composition of Linear Transformation and Matrix Multiplication<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15498&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-11 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.4 Invertibility and Isomorphisms<br \/>\n\u203b\u8a73\u898b\u52d8\u8aa4\u8868-1<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15504&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-12 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">2.5 The Change of Coordinate Matrix<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15510&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-13 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u4e09\u7ae0 Elementary Matrix Operations and Systems of Linear Equations<br \/>\n3.1 Elementary Matrix Operations and Elementary Matrices<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15516&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-14 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.2 The Rank of a Matrix and Matrix Inverses<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15522&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-15 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.3 Systems of Linear Equations-Theoretical Aspects<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15528&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-16 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">3.4 Systems of Linear Equations-Computational Aspects<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15534&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-17 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">\u7b2c\u56db\u7ae0 Determinants<br \/>\n4.1 Determinants of Order 2<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15540&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-18 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.2 Determinants of Order w<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15546&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-19 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.2 Determinants of Order w-\u88dc\u5145<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15553&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-20 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.3 Properties of Determinants<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15558&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-21 odd\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.4 Summary-Important Facts About Determinants<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15564&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<tr class=\"row-22 even\">\n\t<td class=\"column-1\"><\/td><td class=\"column-2\">4.5 A Characterization of the Determinant<\/td><td class=\"column-3\"><a href=\"\/?post_type=course_page&amp;p=15570&amp;lang=en\">Watch Online<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-29 from cache --><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div 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menu-item-object-course_page ajax-mega-menu menu-item-118069\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/school-of-nursing-2\" class=\"elementor-item\" tabindex=\"-1\">School of Nursing<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118071\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-photonics\" class=\"elementor-item\" tabindex=\"-1\">College of Photonics<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-125874\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-biomedical-science-and-engineering\" class=\"elementor-item\" tabindex=\"-1\">College of Biomedical Science and Engineering<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-132738\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/college-of-life-sciences-en\" class=\"elementor-item\" tabindex=\"-1\">College of Life Sciences<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-141797\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/colege-of-medicine-en\" class=\"elementor-item\" tabindex=\"-1\">College of Medicine<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-118072\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-chinese-center\" class=\"elementor-item\" tabindex=\"-1\">Course of Chinese Center<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-120431\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/liberal-arts-college\" class=\"elementor-item\" tabindex=\"-1\">Forum Of Liberal Arts<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123746\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/speech-of-general-education-center\" class=\"elementor-item\" tabindex=\"-1\">Contemporary Civilization<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-128240\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/reading-of-classic-masterpiece\" class=\"elementor-item\" tabindex=\"-1\">Reading of Classic Masterpiece<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-course_page ajax-mega-menu menu-item-123745\"><a href=\"https:\/\/ocw.nycu.edu.tw\/?course_page=all-course-2\/course-of-general-education-center-2\" class=\"elementor-item\" tabindex=\"-1\">Course of General Education Center<\/a><\/li>\n<\/ul>\t\t\t<\/nav>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>4.2 Determinan&hellip;<\/p>\n","protected":false},"featured_media":0,"parent":15289,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","format":"standard","meta":{"footnotes":""},"categories":[965],"tags":[],"class_list":["post-15546","course_page","type-course_page","status-publish","format-standard","hentry","category-linear-algebra-i-100-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.8 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>4.2 Determinants of Order w - NYCU OCW<\/title>\n<meta name=\"description\" content=\"4.2 Determinants of Order w            https:\/\/youtu.be\/ev6i-NCmtUs      Back to Course Homepage       COURSE\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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