{"id":314,"date":"2023-07-06T12:10:47","date_gmt":"2023-07-06T12:10:47","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d8%b9%d8%af%d8%af%d9%8a%d8%a9\/"},"modified":"2023-07-06T12:10:47","modified_gmt":"2023-07-06T12:10:47","slug":"%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d8%b9%d8%af%d8%af%d9%8a%d8%a9","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d8%b9%d8%af%d8%af%d9%8a%d8%a9\/","title":{"rendered":"\u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u062d\u062a\u0649 \u064a\u062a\u0645 \u0641\u0647\u0645\u0647\u0627 \u062a\u0645\u0627\u0645\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0645\u0632\u0627\u064a\u0627 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0639\u0644\u064a\u0647\u0627. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0648\u0636\u062d \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0643\u064a\u0641\u064a\u0629 \u0639\u0643\u0633 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u061f<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff;text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/strong> \u0647\u064a <a href=\"https:\/\/mathority.org\/ar\/\u0645\u0635\u0641\u0648\u0641\u0629-\u0642\u0637\u0631\u064a\u0629\/\"><span style=\"text-decoration: underline;\">\u0645\u0635\u0641\u0648\u0641\u0629 \u0642\u0637\u0631\u064a\u0629<\/span><\/a> \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u062c\u0645\u064a\u0639 \u0627\u0644\u0642\u064a\u0645 \u0639\u0644\u0649 \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0645\u062a\u0633\u0627\u0648\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0647\u0630\u0627 \u0647\u0648 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u0644\u0643\u0646\u0646\u064a \u0645\u062a\u0623\u0643\u062f \u0645\u0646 \u0623\u0646\u0647 \u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0641\u0647\u0645\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0623\u0645\u062b\u0644\u0629: \ud83d\ude09<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2;text-align:right;direction:rtl\"> <span style=\"text-decoration: underline;\">\u0645\u062b\u0627\u0644 \u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 2\u00d72<\/span> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-22152-1.webp\" alt=\"\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u0628\u0639\u062f 2x2\" class=\"wp-image-1910\" width=\"80\" height=\"80\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2;text-align:right;direction:rtl\"> <span style=\"text-decoration: underline;\">\u0645\u062b\u0627\u0644 \u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 3\u00d73<\/span> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-3-dimensionnelle-3-1.webp\" alt=\"\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u0628\u0639\u062f 3x3\" class=\"wp-image-1911\" width=\"116\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2;text-align:right;direction:rtl\"> <span style=\"text-decoration: underline;\">\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0628\u062d\u062c\u0645 4\u00d74<\/span> <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-42154-1.webp\" alt=\"\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u0628\u0639\u062f 4x4\" class=\"wp-image-1912\" width=\"218\" height=\"146\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a \u0623\u064a\u0636\u064b\u0627 \u0645\u0635\u0641\u0648\u0641\u0629 \u0642\u0637\u0631\u064a\u0629\u060c \u0644\u0630\u0644\u0643 \u0633\u062a\u0631\u0649 \u0623\u0646\u0647\u0627 \u062a\u0631\u062b \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u062e\u0635\u0627\u0626\u0635 \u0641\u0626\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0647\u0630\u0647:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a \u0623\u064a\u0636\u064b\u0627<a href=\"https:\/\/mathority.org\/ar\/\u0627\u0654\u0645\u062b\u0644\u0629-\u0648\u062e\u0635\u0627\u064a\u0654\u0635-\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629-\u0627\u0644\u0645\u062a\u0645\u0627\u062b\u0644\u0629\/\">\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0645\u062a\u0645\u0627\u062b\u0644\u0629<\/a> .<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a<a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629-\u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629-\u0627\u0644\u0639\u0644\u0648\u064a\u0629-\u0627\u0644\u0633\u0641\u0644\u064a\u0629\/\">\u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u062b\u0644\u062b\u064a\u0629 \u0639\u0644\u064a\u0627 \u0648\u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u062b\u0644\u062b\u064a\u0629 \u0633\u0641\u0644\u064a\u0629<\/a> .<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/mathority.org\/ar\">\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0647\u0648\u064a\u0629<\/a> \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0623\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0645\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0647\u0648\u064a\u0629 \u0648\u0627\u0644\u0631\u0642\u0645 \u0627\u0644\u0639\u062f\u062f\u064a.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b77f7d177c2769b0847de258adfd1386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 \\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/mathority.org\/ar\/\u0645\u0635\u0641\u0648\u0641\u0629-\u0641\u0627\u0631\u063a\u0629-\u0635\u0641\u0631\/\">\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0635\u0641\u0631\u064a\u0629<\/a> \u0647\u064a \u0623\u064a\u0636\u064b\u0627 \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629.<\/li>\n<\/ul>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629 (\u0623\u0648 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629) \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a \u0639\u0646\u0627\u0635\u0631 \u0642\u0637\u0631\u0647\u0627 \u0627\u0644\u0631\u0626\u064a\u0633\u064a. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0630\u0627\u062a\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0647\u064a \u0646\u0641\u0633\u0647\u0627 \u0648\u0633\u062a\u062a\u0643\u0631\u0631 \u0639\u062f\u0629 \u0645\u0631\u0627\u062a \u0645\u062b\u0644 \u0628\u064f\u0639\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629.<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2513b8d4aeb6d932d9870934102a1637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 8 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 8 \\end{pmatrix} \\longrightarrow \\ \\lambda = 8 \\ ; \\ \\lambda = 8 \\ ; \\ \\lambda = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"298\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0645\u062c\u0627\u0648\u0631\u0629 \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629 \u0623\u062e\u0631\u0649. \u0648\u0623\u0643\u062b\u0631 \u0645\u0646 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0642\u064a\u0645 \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0645\u0631\u0641\u0642\u0629 \u0633\u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0642\u064a\u0645 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0645\u0631\u0641\u0648\u0639\u0629 <em>\u0625\u0644\u0649 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u2013 1<\/em> .<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f7e94cc5a528abace04016dc263c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} \\longrightarrow \\text{Adj}(A)=\\begin{pmatrix} 5^{3-1} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5^{3-1} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5^{3-1} \\end{pmatrix}= \\begin{pmatrix} 25 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 25 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 25 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0645\u0639 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u062d\u062f \u0623\u0633\u0628\u0627\u0628 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0647\u0648 \u0627\u0644\u0633\u0647\u0648\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0633\u0645\u062d \u0644\u0643 \u0628\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629. \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u0641\u0647\u064a \u0645\u0647\u0645\u0629 \u062c\u062f\u064b\u0627 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0644\u0645\u0627\u0630\u0627 \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u062c\u062f\u064b\u0627 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0629:<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062c\u0645\u0639 \u0648\u0637\u0631\u062d \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0646 \u0625\u0636\u0627\u0641\u0629 (\u0648\u0637\u0631\u062d) \u0645\u0635\u0641\u0648\u0641\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646 \u0623\u0645\u0631 \u0628\u0633\u064a\u0637 \u0644\u0644\u063a\u0627\u064a\u0629: \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0625\u0636\u0627\u0641\u0629 (\u0623\u0648 \u0637\u0631\u062d) \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0637\u0627\u0631 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-761de4b4c9bdbbc835b366b21d8cfc2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix} +\\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 7&amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"306\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0636\u0631\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0645\u0639 \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0637\u0631\u062d\u060c \u0644\u062d\u0644 \u0646\u0627\u062a\u062c \u0627\u0644\u0636\u0631\u0628 \u0623\u0648 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0628\u064a\u0646 \u0645\u0635\u0641\u0648\u0641\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0636\u0631\u0628 \u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0623\u0642\u0637\u0627\u0631 \u0628\u064a\u0646\u0647\u0645\u0627. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d30acbf9c6ad31625f8253549e659b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\cdot\\begin{pmatrix} 6 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 6 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} = \\begin{pmatrix} 12 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 12 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 12 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0642\u0648\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0639\u062f \u062d\u0633\u0627\u0628 \u0642\u0648\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0623\u0645\u0631\u064b\u0627 \u0628\u0633\u064a\u0637\u064b\u0627 \u062c\u062f\u064b\u0627 \u0623\u064a\u0636\u064b\u0627: \u0639\u0644\u064a\u0643 \u0631\u0641\u0639 \u0643\u0644 \u0639\u0646\u0635\u0631 \u0642\u0637\u0631\u064a \u0625\u0644\u0649 \u0627\u0644\u0623\u0633. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle\\left. \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix}\\right.^4=\\begin{pmatrix} 2^ 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2^\n\n*** Error message:\nMissing $ inserted.\nleading text: \\displaystyle\nMissing { inserted.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\right. inserted.\nleading text: \\end{document}\n\n<\/pre>\n<p style=\";text-align:right;direction:rtl\"> &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2^4 \\end{pmatrix}= \\begin{pmatrix} 16 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 16 &amp; 0 \\\\[1.1ex] 0 &amp; 0 \u0648 16 \\\u0627\u0644\u0646\u0647\u0627\u064a\u0629 {\u0628\u0645\u0627\u062a\u0631\u064a\u0643\u0633}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca97d1162704371c21b308778890f436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;adsb30&quot; style=&quot; margin:px; text-align:&quot;><\/div>\n<h2 class=&quot;wp-block-heading&quot;> D\u00e9terminant d&#8217;une matrice scalaire<\/h2>\n<p> Calculer le <strong>d\u00e9terminant d&#8217;une matrice scalaire<\/strong> revient \u00e0 r\u00e9soudre le d\u00e9terminant d&#8217;une matrice diagonale : le r\u00e9sultat est le produit des \u00e9l\u00e9ments sur la diagonale principale.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;106&#8243; width=&#8221;582&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\displaystyle \\text{det}(A)= \\prod_{i =1}^n a_i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b3ddf4b77e65a9bd0387f51b7bcaa40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Regardez l'exercice r\u00e9solu suivant dans lequel on trouve le d\u00e9terminant d'une matrice scalaire en multipliant les \u00e9l\u00e9ments de sa diagonale principale :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1099\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7 \\cdot 7 \\cdot 7 = \\bm {343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-773692a573846f155d4c92f1e9075001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" En fait, puisque tous les \u00e9l\u00e9ments de la diagonale principale d'une matrice scalaire sont toujours \u00e9gaux, pour trouver le r\u00e9sultat du d\u00e9terminant, il suffit d'augmenter le num\u00e9ro de la diagonale principale du nombre de fois qu'elle est r\u00e9p\u00e9t\u00e9e. Par cons\u00e9quent, l'exercice pr\u00e9c\u00e9dent peut \u00e9galement \u00eatre r\u00e9solu de la mani\u00e8re suivante :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"2411\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7^3= \\bm{343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d24f9aa91fc9fe8ed74f705f83be3b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D\u00e9montrer ce th\u00e9or\u00e8me est tr\u00e8s simple : il suffit de calculer le d\u00e9terminant d'une matrice scalaire par blocs (ou cofacteurs). Vous trouverez ci-dessous la <strong>d\u00e9monstration<\/strong> de la formule utilisant une matrice scalaire g\u00e9n\u00e9rique :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;62&#8243; width=&#8221;1060&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\begin{aligned} \\begin{vmatrix} a &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; a &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; a \\end{vmatrix}&amp; = a \\cdot \\begin{ vmatrix} a &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} \u2013 0 \\cdot \\begin{vmatrix} 0 &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} + 0 \\cdot \\ \u062a\u0628\u062f\u0623 {vmatrix} 0 &amp; a \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (a\\cdot a) \u2013 0 \\cdot 0 + 0 \\cdot 0 \\\\[ 2ex] &amp; = a \\cdot a \\cdot a \\\\[2ex] &amp; = a^3 \\end{\u0645\u062d\u0627\u0630\u0627\u0629}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc127c7827a5f62c565b8ada378986a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Dans ce cas \u00e7a donne\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"149\" style=\"vertical-align: -1px;\"><\/p>\n<p> \u0623^3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49f5afdd3e1e9918f5323139662a2138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"car la matrice est d'ordre 3, mais il faut toujours l'\u00e9lever \u00e0 l'ordre de la matrice. \n\n<div class=&quot;adsb30&quot; style=&quot; margin:12px; text-align:center&quot;>\n<div id=&quot;ezoic-pub-ad-placeholder-118&quot;><\/div>\n<\/div>\n<h2 class=&quot;wp-block-heading&quot;> Inverser une matrice scalaire<\/h2>\n<p> Une matrice scalaire <strong>est inversible si, et seulement si, tous les \u00e9l\u00e9ments de la diagonale principale sont diff\u00e9rents de 0<\/strong> . Dans ce cas on dit que la matrice scalaire est une matrice r\u00e9guli\u00e8re. De plus, l&#8217;inverse d&#8217;une matrice scalaire sera toujours une autre matrice scalaire avec les <strong>inverses<\/strong> de la diagonale principale :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;174&#8243; width=&#8221;1250&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> \\displaystyle A= \\begin{pmatrix} 9 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 9 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 9 \\end{pmatrix} \\ \\longrightarrow \\ A^{-1 }=\\begin{pmatrix} \\frac{1}{9} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; \\frac{1}{9} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; \\frac{ 1}{9} \\\u0627\u0644\u0646\u0647\u0627\u064a\u0629{\u0628\u0645\u0627\u062a\u0631\u064a\u0643\u0633}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eaf19f57b0cbab7f60c5c1dc0ec45eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, de la caract\u00e9ristique pr\u00e9c\u00e9dente, on peut d\u00e9duire que le d\u00e9terminant d'une matrice scalaire invers\u00e9e est le r\u00e9sultat de la multiplication des inverses de la diagonale principale : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1373\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle B= \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\displaystyle\\left| B^{-1}\\right|=\\cfrac{1}{2} \\cdot \\cfrac{1}{2} \\cdot \\cfrac{1}{2}=\\cfrac{1}{8} = 0.125 \u062f\u0648\u0644\u0627\u0631<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u062d\u062a\u0649 \u064a\u062a\u0645 \u0641\u0647\u0645\u0647\u0627 \u062a\u0645\u0627\u0645\u064b\u0627. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0645\u0632\u0627\u064a\u0627 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0639\u0644\u064a\u0647\u0627. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0648\u0636\u062d \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0643\u064a\u0641\u064a\u0629 \u0639\u0643\u0633 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a. \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u061f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0642\u0637\u0631\u064a\u0629 \u062a\u0643\u0648\u0646 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d8%b9%d8%af%d8%af%d9%8a%d8%a9\/\"> <span class=\"screen-reader-text\">\u0645\u0635\u0641\u0648\u0641\u0629 \u0639\u062f\u062f\u064a\u0629<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f 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