{"id":16047,"date":"2024-01-20T05:29:20","date_gmt":"2024-01-20T01:59:20","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-20T05:29:20","modified_gmt":"2024-01-20T01:59:20","slug":"%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u062d\u0644 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 Numpy \u067e\u0627\u06cc\u062a\u0648\u0646"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%b3%db%8c%d8%b3%d8%aa%d9%85_%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa_%d8%ae%d8%b7%db%8c_%da%86%db%8c%d8%b3%d8%aa%d8%9f\" >\u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0686\u06cc\u0633\u062a\u061f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%ad%d9%84_%db%8c%da%a9_%d8%b3%db%8c%d8%b3%d8%aa%d9%85_%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa_%d8%ae%d8%b7%db%8c_%d8%a8%d8%a7_numpy\" >\u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 Numpy<\/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:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%85%d8%aa%d8%af%d9%87%d8%a7%db%8c_inv_%d9%88_dot\" >\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u062a\u062f\u0647\u0627\u06cc inv() \u0648 dot().<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d8%b1%d9%88%d8%b4sol\" >\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634sol()<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%db%8c%da%a9_%d9%85%d8%ab%d8%a7%d9%84_%d8%af%d8%b1_%d8%af%d9%86%db%8c%d8%a7%db%8c_%d9%88%d8%a7%d9%82%d8%b9%db%8c\" >\u06cc\u06a9 \u0645\u062b\u0627\u0644 \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%ad%d9%84-%d8%b3%db%8c%d8%b3%d8%aa%d9%85-%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa-%d8%ae%d8%b7%db%8c-%d8%a8%d8%a7-numpy-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 4<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<p>\u0627\u06cc\u0646 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/numpy.org\/\">\u0646\u0627\u067e\u062e\u062a\u0647<\/a> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u0646\u0648\u0627\u0639 \u0639\u0645\u0644\u06cc\u0627\u062a \u0631\u06cc\u0627\u0636\u06cc\/\u0639\u0644\u0645\u06cc \u0645\u0627\u0646\u0646\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062a\u0642\u0627\u0637\u0639 \u0648 \u0645\u062d\u0635\u0648\u0644\u0627\u062a \u0646\u0642\u0637\u0647\u060c \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0633\u06cc\u0646\u0648\u0633 \u0648 \u06a9\u0633\u06cc\u0646\u0648\u0633 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fourier_transform\">\u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647<\/a> \u0648 \u062f\u0633\u062a\u06a9\u0627\u0631\u06cc \u0634\u06a9\u0644 \u0648 \u063a\u06cc\u0631\u0647. \u06a9\u0644\u0645\u0647 Numpy \u0646\u0645\u0627\u062f\u06cc \u06a9\u0648\u062a\u0627\u0647 \u0628\u0631\u0627\u06cc &#8220;Numerical Python&#8221; \u0627\u0633\u062a.<\/p>\n<p>\u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0631\u0648\u0634 \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f.<\/p>\n<h2 id=\"whatisasystemoflinearequations\"><span class=\"ez-toc-section\" id=\"%d8%b3%db%8c%d8%b3%d8%aa%d9%85_%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa_%d8%ae%d8%b7%db%8c_%da%86%db%8c%d8%b3%d8%aa%d8%9f\"><\/span>\u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0686\u06cc\u0633\u062a\u061f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0648\u06cc\u06a9\u06cc \u067e\u062f\u06cc\u0627 \u0627\u0644\u0641 \u0631\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/en.wikipedia.org\/wiki\/System_of_linear_equations\">\u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc<\/a> \u0645\u0627\u0646\u0646\u062f:<\/p>\n<blockquote>\n<blockquote>\n<p>\u062f\u0631 \u0631\u06cc\u0627\u0636\u06cc\u0627\u062a\u060c \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc (\u06cc\u0627 \u0633\u06cc\u0633\u062a\u0645 \u062e\u0637\u06cc) \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0627\u06cc \u0627\u0632 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0634\u0627\u0645\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/p>\n<\/blockquote>\n<\/blockquote>\n<p>\u0647\u062f\u0641 \u0646\u0647\u0627\u06cc\u06cc \u0627\u0632 \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc\u060c \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u062c\u0647\u0648\u0644 \u0627\u0633\u062a.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u06cc\u06a9 \u0645\u062b\u0627\u0644 \u0627\u0632 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0645\u062c\u0647\u0648\u0644 \u0622\u0648\u0631\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a. <code>x<\/code> \u0648 <code>y<\/code>:<\/p>\n<p><strong>\u0645\u0639\u0627\u062f\u0644\u0647 1:<\/strong><\/p>\n<pre><code class=\"hljs\">4x  + 3y = 20\n-5x + 9y = 26\n<\/code><\/pre>\n<p>\u0628\u0631\u0627\u06cc \u062d\u0644 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0641\u0648\u0642\u060c \u0628\u0627\u06cc\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 the \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <code>x<\/code> \u0648 <code>y<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627  \u0631\u0627\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u0686\u0646\u06cc\u0646 \u0633\u06cc\u0633\u062a\u0645\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0645\u0627\u0646\u0646\u062f \u062d\u0630\u0641 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u060c \u0642\u0627\u0646\u0648\u0646 \u06a9\u0631\u0627\u0645\u0631\u060c \u062a\u06a9\u0646\u06cc\u06a9 \u06a9\u0627\u0647\u0634 \u0631\u062f\u06cc\u0641 \u0648 \u0631\u0627\u0647 \u062d\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633.  \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u062d\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a.<\/p>\n<p>\u062f\u0631 \u062d\u0644 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\u060c \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0642\u0627\u0628\u0644 \u062d\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0645\u0627\u062a\u0631\u06cc\u0633 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f. <code>AX = B<\/code>.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0646\u0645\u0627\u06cc\u0646\u062f\u06af\u06cc \u06a9\u0646\u06cc\u0645 <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em> \u062f\u0631 \u0642\u0627\u0644\u0628 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0634\u0631\u062d \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">A = (( 4   3)\n     (-5   9))\n\nX = ((x)\n     (y))\n\nB = ((20)\n     (26))\n<\/code><\/pre>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0627\u0631\u0632\u0634 <code>x<\/code> \u0648 <code>y<\/code> \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em>\u060c \u0628\u0627\u06cc\u062f \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u0645 <code>X<\/code>.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0627\u06cc \u0645\u0639\u06a9\u0648\u0633 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u0645 <code>A<\/code>\u060c \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 <code>B<\/code> \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">X = inverse(A).B\n<\/code><\/pre>\n<p>\u0627\u06af\u0631 \u0628\u0627 \u0631\u0648\u0634 \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u0645\u0639\u06a9\u0648\u0633 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0622\u0634\u0646\u0627 \u0646\u06cc\u0633\u062a\u06cc\u062f\u060c \u0628\u0647 \u0627\u06cc\u0646 \u0644\u06cc\u0646\u06a9 \u0646\u06af\u0627\u0647\u06cc \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u062f \u062a\u0627 \u0645\u062a\u0648\u062c\u0647 \u0634\u0648\u06cc\u062f \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u062f\u0633\u062a\u06cc <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse.html\">\u0645\u0639\u06a9\u0648\u0633 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u06a9\u0646\u06cc\u062f<\/a> \u0627\u0632 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633  \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0645\u062d\u0635\u0648\u0644 \u0646\u0642\u0637\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633\u060c \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.mathsisfun.com\/algebra\/matrix-multiplying.html\">\u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647<\/a>.<\/p>\n<h2 id=\"solvingasystemoflinearequationswithnumpy\"><span class=\"ez-toc-section\" id=\"%d8%ad%d9%84_%db%8c%da%a9_%d8%b3%db%8c%d8%b3%d8%aa%d9%85_%d9%85%d8%b9%d8%a7%d8%af%d9%84%d8%a7%d8%aa_%d8%ae%d8%b7%db%8c_%d8%a8%d8%a7_numpy\"><\/span>\u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 Numpy<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u0632 \u0628\u062e\u0634 \u0642\u0628\u0644\u060c \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc\u060c \u0628\u0627\u06cc\u062f \u062f\u0648 \u0639\u0645\u0644 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645: \u0648\u0627\u0631\u0648\u0646\u06af\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0648 \u062d\u0627\u0635\u0644\u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633.  \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u0627\u0632 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0632 \u0647\u0631 \u062f\u0648 \u0639\u0645\u0644\u06cc\u0627\u062a \u067e\u0634\u062a\u06cc\u0628\u0627\u0646\u06cc \u0645\u06cc \u06a9\u0646\u062f.  \u0627\u06af\u0631 \u0642\u0628\u0644\u0627\u064b \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u0631\u0627 \u0646\u0635\u0628 \u0646\u06a9\u0631\u062f\u0647 \u0627\u06cc\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u0648\u0627\u0631\u062f \u0632\u06cc\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f <code>pip<\/code> \u062f\u0633\u062a\u0648\u0631:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-meta\">$<\/span><span class=\"bash\"> pip install numpy<\/span>\n<\/code><\/pre>\n<p>\u062d\u0627\u0644\u0627 \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u06af\u0648\u0646\u0647 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0631\u0627 \u0628\u0627 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u062d\u0644 \u06a9\u0646\u06cc\u0645.<\/p>\n<h3 id=\"usingtheinvanddotmethods\"><span class=\"ez-toc-section\" id=\"%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d9%85%d8%aa%d8%af%d9%87%d8%a7%db%8c_inv_%d9%88_dot\"><\/span>\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0645\u062a\u062f\u0647\u0627\u06cc inv() \u0648 dot().<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0627\u0628\u062a\u062f\u0627 \u0645\u0639\u06a9\u0648\u0633 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06cc\u0627\u0641\u062a <code>A<\/code> \u06a9\u0647 \u062f\u0631 \u0642\u0633\u0645\u062a \u0642\u0628\u0644 \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0631\u062f\u06cc\u0645.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 <code>A<\/code> \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646  \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633\u060c <code>array<\/code> \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0631\u0648\u0634 \u0645\u0627\u0698\u0648\u0644 Numpy \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.  \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0644\u06cc\u0633\u062a\u06cc \u0627\u0632 \u0644\u06cc\u0633\u062a \u0647\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a \u06a9\u0647 \u0647\u0631 \u0644\u06cc\u0633\u062a \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u06cc\u06a9 \u0631\u062f\u06cc\u0641 \u0627\u0633\u062a.<\/p>\n<p>\u062f\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u0644\u06cc\u0633\u062a\u06cc \u0628\u0647 \u0646\u0627\u0645 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>m_list<\/code>\u060c \u06a9\u0647 \u0628\u06cc\u0634\u062a\u0631 \u0634\u0627\u0645\u0644 \u062f\u0648 \u0644\u06cc\u0633\u062a \u0627\u0633\u062a: <code>(4,3)<\/code> \u0648 <code>(-5,9)<\/code>.  \u0627\u06cc\u0646 \u0644\u06cc\u0633\u062a \u0647\u0627 \u062f\u0648 \u0631\u062f\u06cc\u0641 \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0633\u062a\u0646\u062f <code>A<\/code>.  \u0628\u0631\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 <code>A<\/code> \u0628\u0627 Numpy\u060c <code>m_list<\/code> \u0628\u0647 \u0645\u0646\u062a\u0642\u0644 \u0645\u06cc \u0634\u0648\u062f <code>array<\/code> \u0631\u0648\u0634\u06cc \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n\nm_list = ((<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">3<\/span>), (-<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">9<\/span>))\nA = np.array(m_list)\n<\/code><\/pre>\n<p>\u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0639\u06a9\u0648\u0633 \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633\u060c \u0645\u0627\u062a\u0631\u06cc\u0633 \u0628\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0631\u0633\u0627\u0644 \u0645\u06cc \u0634\u0648\u062f <code>linalg.inv()<\/code> \u0631\u0648\u0634 \u0645\u0627\u0698\u0648\u0644 Numpy:<\/p>\n<pre><code class=\"hljs\">inv_A = np.linalg.inv(A)\n\n<span class=\"hljs-built_in\">print<\/span>(inv_A)\n<\/code><\/pre>\n<p>\u0645\u0631\u062d\u0644\u0647 \u0628\u0639\u062f\u06cc \u06cc\u0627\u0641\u062a\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0627\u06cc \u0628\u06cc\u0646 \u0645\u0639\u06a9\u0648\u0633 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0627\u0633\u062a <code>A<\/code>\u060c \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 <code>B<\/code>.  \u0630\u06a9\u0631 \u0627\u06cc\u0646 \u0646\u06a9\u062a\u0647 \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0641\u0642\u0637 \u0628\u06cc\u0646 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627 \u0627\u0645\u06a9\u0627\u0646 \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a <strong>\u0627\u06af\u0631 \u0627\u0628\u0639\u0627\u062f \u062f\u0627\u062e\u0644\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627\u0634\u062f<\/strong> \u06cc\u0639\u0646\u06cc \u062a\u0639\u062f\u0627\u062f \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u0645\u062a \u0686\u067e \u0628\u0627\u06cc\u062f \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u0631\u062f\u06cc\u0641 \u0647\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u0645\u062a \u0631\u0627\u0633\u062a \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u067e\u06cc\u062f\u0627 \u06a9\u0631\u062f\u0646 \u0645\u062d\u0635\u0648\u0644 \u0646\u0642\u0637\u0647 \u0628\u0627 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy\u060c <code>linalg.dot()<\/code> \u062a\u0627\u0628\u0639 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0632\u06cc\u0631 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0646\u0642\u0637\u0647 \u0627\u06cc \u0628\u06cc\u0646 \u0645\u0639\u06a9\u0648\u0633 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0631\u0627 \u067e\u06cc\u062f\u0627 \u0645\u06cc \u06a9\u0646\u062f <code>A<\/code> \u0648 \u0645\u0627\u062a\u0631\u06cc\u0633 <code>B<\/code>\u060c \u06a9\u0647 \u0631\u0627\u0647 \u062d\u0644 \u0627\u0633\u062a <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em>.<\/p>\n<pre><code class=\"hljs\">B = np.array((<span class=\"hljs-number\">20<\/span>, <span class=\"hljs-number\">26<\/span>))\nX = np.linalg.inv(A).dot(B)\n\n<span class=\"hljs-built_in\">print<\/span>(X)\n<\/code><\/pre>\n<p><strong>\u062e\u0631\u0648\u062c\u06cc:<\/strong><\/p>\n<pre><code class=\"hljs\">(2. 4.)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646\u062c\u0627\u060c <code>2<\/code> \u0648 <code>4<\/code> \u0645\u0642\u0627\u062f\u06cc\u0631 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0645\u062c\u0647\u0648\u0644\u0627\u062a \u0647\u0633\u062a\u0646\u062f <code>x<\/code> \u0648 <code>y<\/code> \u06a9\u0647 \u062f\u0631 <em>\u0645\u0639\u0627\u062f\u0644\u0647 1<\/em>.  \u0628\u0631\u0627\u06cc \u062a\u0623\u06cc\u06cc\u062f\u060c \u0627\u06af\u0631 \u0648\u0635\u0644 \u06a9\u0646\u06cc\u062f <code>2<\/code> \u0628\u0647 \u062c\u0627\u06cc \u0646\u0627\u0634\u0646\u0627\u062e\u062a\u0647 <code>x<\/code> \u0648 <code>4<\/code> \u062f\u0631 \u062c\u0627\u06cc \u0646\u0627\u0634\u0646\u0627\u062e\u062a\u0647 <code>y<\/code> \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 <code>4x + 3y<\/code>\u060c \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u06cc\u062f \u06a9\u0647 \u0646\u062a\u06cc\u062c\u0647 20 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0627\u06a9\u0646\u0648\u0646 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0627\u0632 \u0633\u0647 \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u0631\u0627 \u062d\u0644 \u06a9\u0646\u06cc\u0645\u060c \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u062f\u0631 \u0632\u06cc\u0631 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">4x + 3y + 2z = 25\n-2x + 2y + 3z = -10\n3x -5y + 2z = -4\n<\/code><\/pre>\n<p>\u0645\u0639\u0627\u062f\u0644\u0647 \u0641\u0648\u0642 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062d\u0644 \u06a9\u0631\u062f:<\/p>\n<p><strong>\u0645\u0639\u0627\u062f\u0644\u0647 2:<\/strong><\/p>\n<pre><code class=\"hljs\">A = np.array(((<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">2<\/span>), (-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>), (<span class=\"hljs-number\">3<\/span>, -<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">2<\/span>)))\nB = np.array((<span class=\"hljs-number\">25<\/span>, -<span class=\"hljs-number\">10<\/span>, -<span class=\"hljs-number\">4<\/span>))\nX = np.linalg.inv(A).dot(B)\n\n<span class=\"hljs-built_in\">print<\/span>(X)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u0633\u06a9\u0631\u06cc\u067e\u062a \u0628\u0627\u0644\u0627 <code>linalg.inv()<\/code> \u0648 <code>linalg.dot()<\/code> \u0631\u0648\u0634 \u0647\u0627 \u0628\u0647 \u0647\u0645 \u0632\u0646\u062c\u06cc\u0631 \u0634\u062f\u0647 \u0627\u0646\u062f  \u0645\u062a\u063a\u06cc\u0631 <code>X<\/code> \u062d\u0627\u0648\u06cc \u0645\u062d\u0644\u0648\u0644 \u0628\u0631\u0627\u06cc <em>\u0645\u0639\u0627\u062f\u0644\u0647 2<\/em>\u060c \u0648 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0686\u0627\u067e \u0645\u06cc \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">( 5.  3. -2.)\n<\/code><\/pre>\n<p>\u0627\u0631\u0632\u0634 \u0628\u0631\u0627\u06cc \u0645\u062c\u0647\u0648\u0644\u0627\u062a <code>x<\/code>\u060c <code>y<\/code>\u060c \u0648 <code>z<\/code> \u0628\u0647 \u062a\u0631\u062a\u06cc\u0628 5\u060c 3 \u0648 2- \u0647\u0633\u062a\u0646\u062f.  \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0631\u0627 \u0648\u0635\u0644 \u06a9\u0646\u06cc\u062f <em>\u0645\u0639\u0627\u062f\u0644\u0647 2<\/em> \u0648 \u0635\u062d\u062a \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n<h3 id=\"usingthesolvemethod\"><span class=\"ez-toc-section\" id=\"%d8%a8%d8%a7_%d8%a7%d8%b3%d8%aa%d9%81%d8%a7%d8%af%d9%87_%d8%a7%d8%b2_%d8%b1%d9%88%d8%b4sol\"><\/span>\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u0634sol()<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u062f\u0631 \u062f\u0648 \u0645\u062b\u0627\u0644 \u0642\u0628\u0644\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f\u06cc\u0645 <code>linalg.inv()<\/code> \u0648 <code>linalg.dot()<\/code> \u0631\u0648\u0634\u0647\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u062c\u0648\u0627\u0628 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a  \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u0634\u0627\u0645\u0644 <code>linalg.solve()<\/code> \u0631\u0648\u0634\u06cc \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631\u0627\u06cc \u06cc\u0627\u0641\u062a\u0646 \u0645\u0633\u062a\u0642\u06cc\u0645 \u062c\u0648\u0627\u0628 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u0648\u062f:<\/p>\n<pre><code class=\"hljs\">A = np.array(((<span class=\"hljs-number\">4<\/span>, <span class=\"hljs-number\">3<\/span>, <span class=\"hljs-number\">2<\/span>), (-<span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>), (<span class=\"hljs-number\">3<\/span>, -<span class=\"hljs-number\">5<\/span>, <span class=\"hljs-number\">2<\/span>)))\nB = np.array((<span class=\"hljs-number\">25<\/span>, -<span class=\"hljs-number\">10<\/span>, -<span class=\"hljs-number\">4<\/span>))\nX2 = np.linalg.solve(A,B)\n\n<span class=\"hljs-built_in\">print<\/span>(X2)\n<\/code><\/pre>\n<p><strong>\u062e\u0631\u0648\u062c\u06cc:<\/strong><\/p>\n<pre><code class=\"hljs\">( 5.  3. -2.)\n<\/code><\/pre>\n<p>\u0645\u06cc \u0628\u06cc\u0646\u06cc\u062f \u06a9\u0647 \u062e\u0631\u0648\u062c\u06cc \u0645\u0627\u0646\u0646\u062f \u0642\u0628\u0644 \u0627\u0633\u062a.<\/p>\n<h3 id=\"arealworldexample\"><span class=\"ez-toc-section\" id=\"%db%8c%da%a9_%d9%85%d8%ab%d8%a7%d9%84_%d8%af%d8%b1_%d8%af%d9%86%db%8c%d8%a7%db%8c_%d9%88%d8%a7%d9%82%d8%b9%db%8c\"><\/span>\u06cc\u06a9 \u0645\u062b\u0627\u0644 \u062f\u0631 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u062f\u0646\u06cc\u0627\u06cc \u0648\u0627\u0642\u0639\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f.<\/p>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06cc\u06a9 \u0645\u06cc\u0648\u0647\u200c\u0641\u0631\u0648\u0634 \u062f\u0631 \u06cc\u06a9 \u0631\u0648\u0632 20 \u0627\u0646\u0628\u0647 \u0648 10 \u067e\u0631\u062a\u0642\u0627\u0644 \u0631\u0627 \u0628\u0647 \u0645\u0628\u0644\u063a 350 \u062f\u0644\u0627\u0631 \u0641\u0631\u0648\u062e\u062a.  \u0631\u0648\u0632 \u0628\u0639\u062f \u0627\u0648 17 \u0627\u0646\u0628\u0647 \u0648 22 \u067e\u0631\u062a\u0642\u0627\u0644 \u0631\u0627 \u0628\u0647 \u0642\u06cc\u0645\u062a 500 \u062f\u0644\u0627\u0631 \u0641\u0631\u0648\u062e\u062a.  \u0627\u06af\u0631 \u0642\u06cc\u0645\u062a \u0645\u06cc\u0648\u0647 \u0647\u0627 \u0628\u062f\u0648\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0628\u0627\u0642\u06cc \u0645\u06cc \u0645\u0627\u0646\u062f \u0631\u0648\u06cc \u0647\u0631 \u062f\u0648 \u0631\u0648\u0632 \u0642\u06cc\u0645\u062a \u06cc\u06a9 \u0627\u0646\u0628\u0647 \u0648 \u06cc\u06a9 \u067e\u0631\u062a\u0642\u0627\u0644 \u0686\u0646\u062f \u0628\u0648\u062f\u061f<\/p>\n<p>\u0627\u06cc\u0646 \u0645\u0634\u06a9\u0644 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0628\u0627 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u062e\u0637\u06cc \u062d\u0644 \u06a9\u0631\u062f.<\/p>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u0642\u06cc\u0645\u062a \u06cc\u06a9 \u0627\u0646\u0628\u0647 \u0627\u0633\u062a <code>x<\/code> \u0648 \u0642\u06cc\u0645\u062a \u06cc\u06a9 \u067e\u0631\u062a\u0642\u0627\u0644 \u0627\u0633\u062a <code>y<\/code>.  \u0645\u0634\u06a9\u0644 \u0641\u0648\u0642 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">20x + 10y = 350\n17x + 22y = 500\n<\/code><\/pre>\n<p>\u062c\u0648\u0627\u0628 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0641\u0648\u0642 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0646\u0634\u0627\u0646 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">A = np.array(((<span class=\"hljs-number\">20<\/span>, <span class=\"hljs-number\">10<\/span>), (<span class=\"hljs-number\">17<\/span>, <span class=\"hljs-number\">22<\/span>)))\nB = np.array((<span class=\"hljs-number\">350<\/span>, <span class=\"hljs-number\">500<\/span>))\nX = np.linalg.solve(A,B)\n\n<span class=\"hljs-built_in\">print<\/span>(X)\n<\/code><\/pre>\n<p>\u0648 \u0627\u06cc\u0646 \u0647\u0645 \u062e\u0631\u0648\u062c\u06cc:<\/p>\n<pre><code class=\"hljs\">(10. 15.)\n<\/code><\/pre>\n<p>\u062e\u0631\u0648\u062c\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u0642\u06cc\u0645\u062a \u06cc\u06a9 \u0627\u0646\u0628\u0647 10 \u062f\u0644\u0627\u0631 \u0648 \u0642\u06cc\u0645\u062a \u06cc\u06a9 \u067e\u0631\u062a\u0642\u0627\u0644 15 \u062f\u0644\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0631\u0648\u0634 \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u067e\u0627\u06cc\u062a\u0648\u0646 \u062a\u0648\u0636\u06cc\u062d \u0645\u06cc \u062f\u0647\u062f.  \u0634\u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f <code>linalg.inv()<\/code> \u0648 <code>linalg.dot()<\/code> \u0631\u0648\u0634 \u0647\u0627\u06cc \u0632\u0646\u062c\u06cc\u0631\u0647 \u0627\u06cc \u0628\u0631\u0627\u06cc \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc\u060c \u06cc\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f <code>solve()<\/code> \u0631\u0648\u0634.  \u0627\u06cc\u0646 <code>solve()<\/code> \u0631\u0648\u0634\u060c \u0631\u0648\u0634 \u0627\u0631\u062c\u062d \u0627\u0633\u062a.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-20 05:29:14<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;16047&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u062d\u0644 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 Numpy \u067e\u0627\u06cc\u062a\u0648\u0646&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 4<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0627\u06cc\u0646 \u0646\u0627\u067e\u062e\u062a\u0647 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u0646\u0648\u0627\u0639 \u0639\u0645\u0644\u06cc\u0627\u062a \u0631\u06cc\u0627\u0636\u06cc\/\u0639\u0644\u0645\u06cc \u0645\u0627\u0646\u0646\u062f \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u062a\u0642\u0627\u0637\u0639 \u0648 \u0645\u062d\u0635\u0648\u0644\u0627\u062a \u0646\u0642\u0637\u0647\u060c \u06cc\u0627\u0641\u062a\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u0633\u06cc\u0646\u0648\u0633 \u0648 \u06a9\u0633\u06cc\u0646\u0648\u0633 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f. \u062a\u0628\u062f\u06cc\u0644 \u0641\u0648\u0631\u06cc\u0647 \u0648 \u062f\u0633\u062a\u06a9\u0627\u0631\u06cc \u0634\u06a9\u0644 \u0648 \u063a\u06cc\u0631\u0647. \u06a9\u0644\u0645\u0647 Numpy \u0646\u0645\u0627\u062f\u06cc \u06a9\u0648\u062a\u0627\u0647 \u0628\u0631\u0627\u06cc &#8220;Numerical Python&#8221; \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0631\u0648\u0634 \u062d\u0644 \u06cc\u06a9 \u0633\u06cc\u0633\u062a\u0645 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062e\u0637\u06cc \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 Numpy \u067e\u0627\u06cc\u062a\u0648\u0646 \u0631\u0627 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":9162,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-16047","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16047","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=16047"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/16047\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/9162"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=16047"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=16047"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=16047"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}