{"id":2122,"date":"2026-07-30T16:54:42","date_gmt":"2026-07-30T08:54:42","guid":{"rendered":"https:\/\/www.math.ntnu.edu.tw\/merc\/?page_id=2122"},"modified":"2026-07-30T16:59:36","modified_gmt":"2026-07-30T08:59:36","slug":"%e7%b7%9a%e6%80%a7%e8%ae%8a%e6%8f%9b%e7%9a%84%e7%89%b9%e6%80%a7","status":"publish","type":"page","link":"https:\/\/www.math.ntnu.edu.tw\/merc\/animated_math\/%e7%b7%9a%e6%80%a7%e8%ae%8a%e6%8f%9b%e7%9a%84%e7%89%b9%e6%80%a7\/","title":{"rendered":"\u7dda\u6027\u8b8a\u63db\u7684\u7279\u6027"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2122\" class=\"elementor elementor-2122\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2ac49eed e-flex e-con-boxed e-con e-parent\" data-id=\"2ac49eed\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-78325777 elementor-invisible elementor-widget elementor-widget-heading\" data-id=\"78325777\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;bounceIn&quot;}\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u821e\u52d5\u6578\u5b78<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6c7cab53 e-flex e-con-boxed e-con e-parent\" data-id=\"6c7cab53\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-175dbc13 elementor-widget elementor-widget-heading\" data-id=\"175dbc13\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">\u7dda\u6027\u8b8a\u63db\u7684\u7279\u6027<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1911b6f3 e-flex e-con-boxed e-con e-parent\" data-id=\"1911b6f3\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-44f7b5cb elementor-widget elementor-widget-video\" data-id=\"44f7b5cb\" data-element_type=\"widget\" data-e-type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;autoplay&quot;:&quot;yes&quot;,&quot;loop&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/cantor.math.ntnu.edu.tw\/workshop\/animated_math\/media\/\u7dda\u6027\u8b8a\u63db\u7684\u7279\u6027.mp4\" autoplay=\"\" loop=\"\" controls=\"\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2f732889 e-flex e-con-boxed e-con e-parent\" data-id=\"2f732889\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-656277b5 elementor-widget elementor-widget-text-editor\" data-id=\"656277b5\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>\u7dda\u6027\u8b8a\u63db\u7684\u7279\u6027<\/h3>\n<p>\u9019\u90e8\u6559\u5b78\u5f71\u7247\u4e3b\u8981\u63a2\u8a0e\u5e73\u9762\u7dda\u6027\u8b8a\u63db\uff08\u4e8c\u968e\u65b9\u9663 $A$\uff09\u7684\u5e7e\u4f55\u7279\u6027\uff0c\u4e26\u4f9d\u64da\u77e9\u9663\u7684\u884c\u5217\u5f0f\u503c\uff08$\\det(A)$\uff09\u5340\u5206\u70ba\u4ee5\u4e0b\u5e7e\u7a2e\u60c5\u5f62\uff1a<\/p>\n<ol>\n<li>\u884c\u5217\u5f0f\u4e0d\u7b49\u65bc 0 ($\\det(A) \\neq 0$)\n <ul>\n  <li>\u5e7e\u4f55\u610f\u7fa9\uff1a\u5c07\u5e73\u9762\u5c0d\u61c9\u5230\u5e73\u9762\u3002<\/li>\n  <li>\u7279\u6027\uff1a\n    <ul>\n     <li>\u6703\u5c07\u96f6\u5411\u91cf\u5c0d\u61c9\u5230\u96f6\u5411\u91cf\u3002<\/li>\n     <li>\u6703\u5c07\u57fa\u6e96\u5411\u91cf $(1,0)$ \u5c0d\u61c9\u5230\u7b2c\u4e00\u884c\u5411\u91cf $\\begin{pmatrix} a \\\\ c \\end{pmatrix}$\uff0c\u5c07 $(0,1)$ \u5c0d\u61c9\u5230\u7b2c\u4e8c\u884c\u5411\u91cf $\\begin{pmatrix} b \\\\ d \\end{pmatrix}$\u3002<\/li>\n     <li>\u7dda\u6027\u7d44\u5408\u7684\u4fc2\u6578\u4fdd\u6301\u4e0d\u8b8a\uff1a\u5411\u91cf $(x,y) = x(1,0) + y(0,1)$ \u6703\u88ab\u8b8a\u63db\u70ba $x\\begin{pmatrix} a \\\\ c \\end{pmatrix} + y\\begin{pmatrix} b \\\\ d \\end{pmatrix}$\u3002<\/li>\n    <\/ul>\n  <\/li>\n <\/ul>\n<\/li>\n<li>\u884c\u5217\u5f0f\u7b49\u65bc 0 ($\\det(A) = 0$)\n <ul>\n  <li>\u975e\u96f6\u77e9\u9663\uff08\u5982 $A = \\begin{pmatrix} 1 &#038; 2 \\\\ 2 &#038; 4 \\end{pmatrix}$\uff09\uff1a\n    <ul>\n      <li>\u5e7e\u4f55\u610f\u7fa9\uff1a\u5c07\u6574\u500b\u5e73\u9762\u5c0d\u61c9\u5230\u4e00\u689d\u904e\u539f\u9ede\u7684\u76f4\u7dda\uff08\u964d\u7dad\uff09\u3002<\/li>\n      <li>\u7279\u6027\uff1a\u539f\u672c\u843d\u5728\u540c\u4e00\u689d\u5e73\u884c\u7dda\uff08\u5982 $x+2y=k$\uff09\u4e0a\u7684\u9ede\u6216\u5411\u91cf\uff0c\u7d93\u8b8a\u63db\u5f8c\u90fd\u6703\u6620\u5c04\u5230\u540c\u4e00\u689d\u76f4\u7dda\u4e0a\u7684\u7279\u5b9a\u9ede\u6216\u5411\u91cf\uff08\u5982 $k(1,2)$\uff09\u3002<\/li>\n    <\/ul>\n  <\/li>\n  <li>\u96f6\u77e9\u9663\uff08$A = \\begin{pmatrix} 0 &#038; 0 \\\\ 0 &#038; 0 \\end{pmatrix}$\uff09\uff1a\n    <ul>\n     <li>\u5e7e\u4f55\u610f\u7fa9\uff1a\u5c07\u6574\u500b\u5e73\u9762\u4e0a\u7684\u6240\u6709\u5411\u91cf\u8207\u9ede\u90fd\u5c0d\u61c9\u5230\u539f\u9ede\uff08\u96f6\u5411\u91cf\uff09\u3002<\/li>\n    <\/ul>\n  <\/li>\n <\/ul>\n<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2703dd14 e-flex e-con-boxed e-con e-parent\" data-id=\"2703dd14\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1523522 elementor-widget elementor-widget-text-editor\" data-id=\"1523522\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a style=\"font-size: 18px; color: red;\" 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[&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":193,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"full-width","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-2122","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/2122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/comments?post=2122"}],"version-history":[{"count":7,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/2122\/revisions"}],"predecessor-version":[{"id":2130,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/2122\/revisions\/2130"}],"up":[{"embeddable":true,"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/pages\/193"}],"wp:attachment":[{"href":"https:\/\/www.math.ntnu.edu.tw\/merc\/wp-json\/wp\/v2\/media?parent=2122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}