{"id":987,"date":"2024-03-22T11:40:40","date_gmt":"2024-03-22T05:40:40","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=987"},"modified":"2024-11-03T21:17:34","modified_gmt":"2024-11-03T15:17:34","slug":"types-of-matrix","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/types-of-matrix\/","title":{"rendered":"\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09be\u09b0\u09ad\u09c7\u09a6 (Types of matrix)"},"content":{"rendered":"<h2><span style=\"color: #339966;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Matrix) \u0995\u09be\u0995\u09c7 \u09ac\u09b2\u09c7? \u0995\u09a4 \u09aa\u09cd\u09b0\u0995\u09be\u09b0 \u0993 \u0995\u09bf \u0995\u09bf?<\/b><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u0995\u09be\u0995\u09c7 \u09ac\u09b2\u09c7? \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8 \u0993<span style=\"color: #0000ff;\"> <a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/math-series\/\">\u0997\u09a3\u09bf\u09a4<\/a><\/span> \u098f\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a4\u09a5\u09cd\u09af \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09b8\u09be\u09b0\u09bf (\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09b0\u09c7\u0996\u09be) \u0993 \u0995\u09b2\u09be\u09ae (\u0989\u09b2\u09ae\u09cd\u09ac \u09b0\u09c7\u0996\u09be) \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u09be\u099c\u09be\u09b2\u09c7 \u09af\u09c7 \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09ac\u09bf\u09a8\u09cd\u09af\u09be\u09b8 (rectangular arrays) \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u098f\u0995\u09c7 <strong>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/strong> \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter\" src=\"https:\/\/maths.olympiadsuccess.com\/assets\/images\/maths_square_dictionary\/matrix.jpg\" alt=\"\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u0995\u09be\u0995\u09c7 \u09ac\u09b2\u09c7?\" width=\"300\" height=\"230\" \/><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09b8\u09be\u09b0\u09bf \u0993 \u0995\u09b2\u09be\u09ae (Rows &amp; Columns of Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09ac\u09bf\u09a8\u09cd\u09af\u09be\u09b8\u0995\u09c7<strong> \u09a6\u09c1\u0987 \u09aa\u09cd\u09b0\u0995\u09be\u09b0\u09c7<\/strong> \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u09af\u09a5\u09be: \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u098f\u09ac\u0982 \u0989\u09b2\u09ae\u09cd\u09ac \u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0\u0964 \u09b8\u0982\u0996\u09cd\u09af\u09be\u0997\u09c1\u09b2\u09bf\u09b0 \u0986\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09b2\u09c7\u0996\u09be\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u09b8\u09be\u09b0\u09bf \u098f\u09ac\u0982 \u0989\u09b2\u09ae\u09cd\u09ac \u09b0\u09c7\u0996\u09be\u0997\u09c1\u09b2\u09bf\u0995\u09c7 \u0995\u09b2\u09be\u09ae \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0995\u09cd\u09b0\u09ae (Order of Matrix) <\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">m<\/span><span style=\"font-weight: 400;\"> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u09b8\u09be\u09b0\u09bf \u0993 <\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u09b8\u0982\u0996\u09cd\u09af\u0995 \u0995\u09b2\u09be\u09ae \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u0995\u09cb\u09a8\u09cb \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7 <\/span><strong>m\u00d7n (m \u09ac\u09be\u0987 n<\/strong><span style=\"font-weight: 400;\"><strong>)<\/strong> \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 <span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/www.youtube.com\/watch?v=w5NRpyGBPWA&amp;list=PL0dr4HGr8HPjbTz1tOzTYdUTKm8A49qAf\" target=\"_blank\" rel=\"noopener\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/a><\/span> \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 <\/span><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf \u09b8\u0982\u0996\u09cd\u09af\u09be \u098f\u09b0 \u09b8\u09be\u09b0\u09bf \u0993 \u0995\u09b2\u09be\u09ae\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09af\u09bc\u0964\u00a0<\/span><\/p>\n<h2><span style=\"color: #339966;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09be\u09b0\u09ad\u09c7\u09a6 (Types of matrix)<\/b><\/span><\/h2>\n<h3><span style=\"color: #800080;\"><b>\u09b8\u09be\u09b0\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Row Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0995\u09c7\u09ac\u09b2 \u098f\u0995\u099f\u09bf \u09b8\u09be\u09b0\u09bf \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u0995\u09c7 \u09b8\u09be\u09b0\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u0995\u09b2\u09ae \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Column Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0995\u09c7\u09ac\u09b2 \u098f\u0995\u099f\u09bf \u0995\u09b2\u09be\u09ae \u09ac\u09bf\u09a6\u09cd\u09af\u09ae\u09be\u09a8 \u09a5\u09be\u0995\u09c7 \u09a4\u09be\u0995\u09c7 \u0995\u09b2\u09be \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Square Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09b8\u09be\u09b0\u09bf \u0993 \u0995\u09b2\u09be\u09ae\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b8\u09ae\u09be\u09a8 \u09a4\u09be\u0995\u09c7 \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964 \u09af\u09c7\u09ae\u09a8:<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{bmatrix}\n\na_{11} &amp; a_{12} &amp; a_{13}\\\\\n\na_{21} &amp; a_{21} &amp; a_{23}\\\\\n\na_{31} &amp; a_{32} &amp; a_{33}\n\n\\end{bmatrix}<\/span>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf <\/span><strong>3\u00d73<\/strong><span style=\"font-weight: 400;\"> \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u09ac\u09be \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 <\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 <strong>\u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/strong>\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3 (Principal Diagonal)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times n}<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u0995\u099f\u09bf n \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0964 \u098f\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">a_{11}, a_{22}, a_{33},..., a_{nn}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ad\u0995\u09cd\u09a4\u09bf\u0997\u09c1\u09b2\u09cb \u09a8\u09bf\u09af\u09bc\u09c7 \u09af\u09c7 \u09ac\u09b0\u09cd\u0997 \u0997\u09a0\u09bf\u09a4 \u09a4\u09be\u0995\u09c7 \u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u098a\u09b0\u09cd\u09a7\u09cd\u09ac \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09be\u0995\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Upper Triangular Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times n}<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u09a8\u09bf\u09ae\u09cd\u09a8\u09b8\u09cd\u09a5 \u09b8\u09ac\u0997\u09c1\u09b2\u09bf \u09ad\u09c1\u0995\u09cd\u09a4\u09bf 0 \u09b9\u09b2\u09c7 ( \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09af\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">i&lt;j<\/span><span style=\"font-weight: 400;\">) \u09a4\u09be\u0995\u09c7 \u098a\u09b0\u09cd\u09a7\u09cd\u09ac \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09be\u0995\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09a8\u09bf\u09ae\u09cd\u09a8 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09be\u0995\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Lower Triangular Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times n}<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u0989\u09aa\u09b0 \u09b8\u09ac\u0997\u09c1\u09b2\u09cb \u09ad\u09c1\u0995\u09cd\u09a4\u09bf 0 \u09b9\u09b2\u09c7 ( \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09af\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">i&lt;j<\/span><span style=\"font-weight: 400;\">) \u09a4\u09be\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8 \u09a4\u09cd\u09b0\u09bf\u09ad\u09c1\u099c\u09be\u0995\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u0995\u09b0\u09cd\u09a3 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Diagonal Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <\/span><span style=\"font-weight: 400;\">A=<\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">ij<\/span><span style=\"font-weight: 400;\">m\u00d7m<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 m \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <\/span><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">ij<\/span><span style=\"font-weight: 400;\">=0<\/span><span style=\"font-weight: 400;\"> \u09b9\u09af\u09bc \u09af\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">i<\/span><span style=\"font-weight: 400;\">j<\/span><span style=\"font-weight: 400;\"> \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf \u09ac\u09cd\u09af\u09a4\u09c0\u09a4 \u0985\u09aa\u09b0 \u09b8\u0995\u09b2 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf (0) \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b8\u09cd\u0995\u09c7\u09b2\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Scalar Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u0995\u09b0\u09cd\u09a3 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0985\u09b6\u09c2\u09a8\u09cd\u09af \u09ad\u09c1\u0995\u09cd\u09a4\u09bf\u0997\u09c1\u09b2\u09cb \u09b8\u09ae\u09be\u09a8 \u09b9\u09b2\u09c7, \u0993\u0987 \u0995\u09b0\u09cd\u09a3 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7 \u09b8\u09cd\u0995\u09c7\u09b2\u09be\u09b0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u098f\u0995\u0995 \u09ac\u09be \u0985\u09ad\u09c7\u09a6\u0995 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Identity Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{m\\times m}<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 m \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u098f\u0995\u0995 \u09ac\u09be \u0985\u09ad\u09c7\u09a6\u0995 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09af\u09be\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">i \\ne j<\/span><\/span><span style=\"font-weight: 400;\"> \u09af\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=1<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 \u09af\u0996\u09a8 <\/span><span style=\"font-weight: 400;\">i=j \u098f\u09b0 \u099c\u09a8\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u09ac\u09be \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf \u09ac\u09cd\u09af\u09a4\u09c0\u09a4 \u0985\u09aa\u09b0 \u09b8\u0995\u09b2 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf (0) \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09a7\u09be\u09a8 \u0995\u09b0\u09cd\u09a3\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf 1 \u09b9\u09b2\u09c7 \u09a4\u09be\u0995\u09c7 \u0985\u09ad\u09c7\u09a6\u0995 \u09ac\u09be \u098f\u0995\u0995 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b6\u09c2\u09a8\u09cd\u09af \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Null Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09b8\u0995\u09b2 \u09ad\u09c1\u0995\u09cd\u09a4\u09bf 0 \u09b9\u09b2\u09c7 \u09a4\u09be\u0995\u09c7 \u09b6\u09c2\u09a8\u09cd\u09af \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b8\u09ae\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Idempotent Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09ac\u09b0\u09cd\u0997\u09be\u0995\u09be\u09b0 \u0995\u09cb\u09a8\u09cb \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7 \u09b8\u09ae\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^2=A<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b6\u09c2\u09a8\u09cd\u09af\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Nilpotent Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 A \u0995\u09c7 \u09b6\u09c2\u09a3\u09cd\u09af\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^n=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09af\u09bc \u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span><span style=\"font-weight: 400;\">n\u2208N\u0964<\/span><span style=\"font-weight: 400;\"> \u09af\u09a6\u09bf \u09b8\u09b0\u09cd\u09ac\u09a8\u09bf\u09ae\u09cd\u09a8 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09aa\u09c2\u09b0\u09cd\u09a3 \u09b8\u0982\u0996\u09cd\u09af\u09be n \u098f\u09b0 \u099c\u09a8\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">A^n=0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u09b9\u09af\u09bc, \u09a4\u09ac\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 A \u0995\u09c7 n \u098f\u09b0 \u09b6\u09c2\u09a3\u09cd\u09af\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09df\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u0985\u09ad\u09c7\u09a6\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Involutory\u00a0Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u0995\u09c7 \u0985\u09ad\u09c7\u09a6\u0998\u09be\u09a4\u09bf \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^2=I<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09aa\u09cb\u09b8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Transpose Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u09af\u09a5\u09be\u09af\u09a5 \u09b8\u09be\u09b0\u09bf \u098f\u09ac\u0982 \u0995\u09b2\u09be\u09ae \u09ac\u09bf\u09a8\u09bf\u09ae\u09af\u09bc \u0995\u09b0\u09b2\u09c7 \u09af\u09c7 \u09a8\u09a4\u09c1\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09aa\u09cb\u09b8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09aa\u09cb\u09b8 \u09ae\u09c7\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">A^+<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09be <span class=\"katex-eq\" data-katex-display=\"false\">A'<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a7\u09b0\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">A=\\begin{bmatrix}\n\n-1 &amp; 0 &amp; 1\\\\\n\n2 &amp; 3 &amp; 0\\\\\n\n4 &amp; 1 &amp; 3\n\n\\end{bmatrix}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09b2\u09c7<\/span><span style=\"font-weight: 400;\">, <span class=\"katex-eq\" data-katex-display=\"false\">A^+=\\begin{bmatrix}\n\n-1 &amp; 2 &amp; 4\\\\\n\n0 &amp; 3 &amp; 1\\\\\n\n1 &amp; 0 &amp; 3\n\n\\end{bmatrix}<\/span><\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae<\/b> <b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Symmetric Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b0\u09cd\u0997<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times m\\n}<\/span> <span style=\"font-weight: 400;\">\u0995\u09c7<\/span> <span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09ac\u09c7<\/span> <span style=\"font-weight: 400;\">\u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^+=A'<\/span> <\/span><span style=\"font-weight: 400;\">\u09b9\u09af\u09bc<\/span> <span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=a_{ji}<\/span>\u00a0<span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae<\/b> <b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/b><b><i>\u00a0<\/i>(Skew Symmetric)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b0\u09cd\u0997<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times m\\n}<\/span>\u00a0<span style=\"font-weight: 400;\">\u0995\u09c7<\/span> <span style=\"font-weight: 400;\">\u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09ac\u09c7<\/span> <span style=\"font-weight: 400;\">\u09af\u09a6\u09bf<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">A^+=-A'<\/span>\u00a0<span style=\"font-weight: 400;\">\u09b9\u09af\u09bc<\/span> <span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=-a_{ji}<\/span> <span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span> <span style=\"font-weight: 400;\">\u0989\u09b2\u09cd\u09b2\u09c7\u0996\u09cd\u09af<\/span> <span style=\"font-weight: 400;\">\u09af\u09c7<\/span> <span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a7\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u0995\u09b0\u09cd\u09a3\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09ad\u09c1\u0995\u09cd\u09a4\u09bf<\/span> <span style=\"font-weight: 400;\">\u09b8\u09ae\u09c2\u09b9<\/span><i><span style=\"font-weight: 400;\"> 0 <\/span><\/i><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=0<\/span> <span style=\"font-weight: 400;\">\u09af\u0996\u09a8<\/span> <span style=\"font-weight: 400;\">i=j<\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u0989\u09aa-\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Sub Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb<\/span> <span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09af\u09c7\u0995\u09cb\u09a8\u09cb<\/span> <span style=\"font-weight: 400;\">\u09b8\u0982\u0996\u09cd\u09af\u0995<\/span> <span style=\"font-weight: 400;\">\u0995\u09b2\u09be\u09ae<\/span> <span style=\"font-weight: 400;\">\u0993<\/span> <span style=\"font-weight: 400;\">\u09b8\u09be\u09b0\u09bf\u09b0<\/span> <span style=\"font-weight: 400;\">\u09ad\u09c1\u0995\u09cd\u09a4\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ac\u09be\u09a6<\/span> <span style=\"font-weight: 400;\">\u09a6\u09bf\u09af\u09bc\u09c7<\/span> <span style=\"font-weight: 400;\">\u0997\u09a0\u09bf\u09a4<\/span> <span style=\"font-weight: 400;\">\u0986\u09b0\u09c7\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7<\/span> <span style=\"font-weight: 400;\">\u09ae\u09c2\u09b2<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u0989\u09aa-\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b2\u09ae\u09cd\u09ac<\/b> <b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Normal Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u098f\u0995\u099f\u09bf<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b0\u09cd\u0997<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span style=\"font-weight: 400;\">A<\/span> <span style=\"font-weight: 400;\">\u0995\u09c7<\/span> <span style=\"font-weight: 400;\">\u09b2\u09ae\u09cd\u09ac<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09ac\u09c7<\/span> <span style=\"font-weight: 400;\">\u09af\u09a6\u09bf<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">AA^+=A^+A=I<\/span>\u00a0<span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/b> <b>\u099f\u09cd\u09b0\u09c7\u09b8 (Trace of a Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb<\/span> <span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09a7\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09be<\/span> <span style=\"font-weight: 400;\">\u09ae\u09c2\u0996\u09cd\u09af<\/span> <span style=\"font-weight: 400;\">\u0995\u09b0\u09cd\u09a3\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09ad\u09c1\u0995\u09cd\u09a4\u09bf<\/span> <span style=\"font-weight: 400;\">\u09b8\u09ae\u09c2\u09b9\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u09af\u09cb\u0997\u09ab\u09b2\u0995\u09c7<\/span> \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0\u00a0<span style=\"font-weight: 400;\">\u099f\u09cd\u09b0\u09c7\u09b8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0<\/b> <b>\u09b8\u09ae\u09a4\u09be (Equivalence of Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09a6\u09c1\u099f\u09bf<\/span> \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8<span style=\"font-weight: 400;\">\u0995\u09c7<\/span> <span style=\"font-weight: 400;\">\u09b8\u09ae\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u09ac\u09b2\u09be<\/span> <span style=\"font-weight: 400;\">\u09b9\u09ac\u09c7<\/span> <span style=\"font-weight: 400;\">\u09af\u09a6\u09bf<\/span> <span style=\"font-weight: 400;\">\u098f\u09a6\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u0995\u09cd\u09b0\u09ae<\/span> <span style=\"font-weight: 400;\">\u09b8\u09ae\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u09b9\u09af\u09bc<\/span> <span style=\"font-weight: 400;\">\u098f\u09ac\u0982<\/span> <span style=\"font-weight: 400;\">\u0989\u09ad\u09af\u09bc\u09c7\u09b0<\/span> <span style=\"font-weight: 400;\">\u0985\u09a8\u09c1\u09b0\u09c2\u09aa<\/span> <span style=\"font-weight: 400;\">\u09ad\u09c1\u0995\u09cd\u09a4\u09bf<\/span><span style=\"font-weight: 400;\">\u09b8\u09ae\u09c2\u09b9<\/span> <span style=\"font-weight: 400;\">\u09aa\u09b0\u09b8\u09cd\u09aa\u09b0<\/span> <span style=\"font-weight: 400;\">\u09b8\u09ae\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Hermitian Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09bf\u0995\u09cd\u09b8 <span class=\"katex-eq\" data-katex-display=\"false\">A=(a_{ij})_{n\\times m\\n}<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^{\\theta}=A<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=\\bar{a_{ij}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09df \u09b8\u0995\u09b2 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">1\\leq i, j\\leq n<\/span><\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u099c\u09a8\u09cd\u09af\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09ae\u09a8:<\/span><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">A=\\begin{bmatrix}\n\n2 &amp; 3+i &amp; 4+i\\\\\n\n3-i &amp; 4 &amp; 3+2i\\\\\n\n4-i &amp; 3-2i &amp; 6\n\n\\end{bmatrix}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore A^T=\\begin{bmatrix}\n\n2 &amp; 3-i &amp; 4-i\\\\\n\n3+i &amp; 4 &amp; 3-2i\\\\\n\n4+i &amp; 3+2i &amp; 6\n\n\\end{bmatrix}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore A^{\\theta} = \\bar{A^T} =\\begin{bmatrix}\n\n2 &amp; 3-i &amp; 4-i\\\\\n\n3+i &amp; 4 &amp; 3-2i\\\\\n\n4+i &amp; 3+2i &amp; 6\n\n\\end{bmatrix}=A<\/span>\n<p><b>Note:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">(i) \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u0995\u09b0\u09cd\u09a3 \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u0995\u09b2 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9 \u0985\u09ac\u09b6\u09cd\u09af\u0987 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(ii) \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 <\/span><span style=\"font-weight: 400;\">A\u00a0<\/span><span style=\"font-weight: 400;\">\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">A=A^{\\theta}<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Inverse Hermitian Matrix)<\/b><\/span><\/h3>\n<p><b> <\/b><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09bf\u0995\u09cd\u09b8 <span class=\"katex-eq\" data-katex-display=\"false\">a=[a_{ij}]_{n\\times n}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4<\/span> <span style=\"font-weight: 400;\">\u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09df\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">A^{\\theta}=-A<\/span><\/span><span style=\"font-weight: 400;\"> \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">a_{ij}=-\\bar{a_{ij}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09b9\u09df, \u09b8\u0995\u09b2 <\/span><span style=\"font-weight: 400;\">1\u2264i,\u00a0j\u2264n<\/span><span style=\"font-weight: 400;\"> \u098f\u09b0 \u099c\u09a8\u09cd\u09af\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09ae\u09a8 :\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">A=\\begin{bmatrix}\n\n2i &amp; -2-3i &amp; -2+i\\\\\n\n2-3i &amp; -i &amp; 3i\\\\\n\n2+i &amp; 3i &amp; 0\n\n\\end{bmatrix}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore A^T=\\begin{bmatrix}\n\n2i &amp; 2-3i &amp; 2+i\\\\\n\n2-3i &amp; -i &amp; 3i\\\\\n\n-2+i &amp; 3i &amp; 0\n\n\\end{bmatrix}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\therefore A^{\\theta}=\\bar{A^T}=-A<\/span>\n<p><b>Note :<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ae\u09c1\u0996\u09cd\u09af \u0995\u09b0\u09cd\u09a3 \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u0995\u09b2 \u0989\u09aa\u09be\u09a6\u09be\u09a8 \u09b8\u09ae\u09c2\u09b9 \u0985\u09ac\u09b6\u09cd\u09af\u0987 \u09b8\u09ae\u09cd\u09aa\u09c2\u09b0\u09cd\u09a3 \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u09ac\u09be \u09b6\u09c2\u09a8\u09cd\u09af \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09af\u09c7\u0995\u09cb\u09a8 \u09ac\u09b0\u09cd\u0997 A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">A-A^{\\theta}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">( \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u09af\u09c7\u0995\u09cb\u09a8 \u09ac\u09b0\u09cd\u0997 A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09b8\u09ae\u09c2\u09b9 \u099c\u099f\u09bf\u09b2 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09b9\u09b2\u09c7 A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ae\u09be\u09a4\u09cd\u09b0 \u0989\u09aa\u09be\u09af\u09bc\u09c7 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u098f\u09ac\u0982 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09af\u09cb\u0997\u09ab\u09b2 \u0986\u0995\u09be\u09b0\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09be\u09ac\u09c7\u0964\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">A=\\frac{1}{2}(A+A^{\\theta})+\\frac{1}{2}(A-A^{\\theta})<\/span><\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h3><span style=\"color: #800080;\"><b>\u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u098f\u09ac\u0982 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09cd\u09af :\u00a0<\/b><\/span><\/h3>\n<ul>\n<li><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf A \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">AA^{\\theta}<\/span> <\/span><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">A^{\\theta}A<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/span><\/li>\n<li>\u09af\u09a6\u09bf A \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7\u2212<\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u00a0= <\/span><span style=\"font-weight: 400;\">iA<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964 <\/span><\/p>\n<p>= <span class=\"katex-eq\" data-katex-display=\"false\">\\bar{A}<\/span> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/p>\n<p>= kA \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964 \u09af\u09c7\u0996\u09be\u09a8\u09c7 k\u2208R<\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf A \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">= iA \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <span class=\"katex-eq\" data-katex-display=\"false\">\\bar{A}<\/span> \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= kA \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf A \u098f\u09ac\u0982 B \u098f\u0995\u0987 \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">= <span class=\"katex-eq\" data-katex-display=\"false\">k_1A+k_2B<\/span> \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0993 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7 \u09af\u09c7\u0996\u09be\u09a8\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">k_1,k_2\\epsilon R<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (AB)<\/span><span style=\"font-weight: 400;\"> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7 \u09af\u09a6\u09bf <\/span><span style=\"font-weight: 400;\">AB=BA<\/span><span style=\"font-weight: 400;\"> \u09b9\u09af\u09bc\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (AB+BA)<\/span><span style=\"font-weight: 400;\"> \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (AB \u2013 BA)<\/span><span style=\"font-weight: 400;\"> \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf A \u098f\u09ac\u0982 B \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995\u09c7\u0987 \u098f\u0995\u0987 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">k_1A+k_2B<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b9\u09be\u09b0\u09ae\u09bf\u09b8\u09bf\u09af\u09bc\u09be\u09a8 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/span><\/li>\n<\/ul>\n<h3><span style=\"color: #800080;\"><b>\u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Unitary Matrix)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8 \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09a4\u09be\u09b0 \u0985\u09a8\u09c1\u09ac\u09a8\u09cd\u09a7\u09c0 \u09ac\u09bf\u09ae\u09cd\u09ac \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u0997\u09c1\u09a3 \u0995\u09b0\u09b2\u09c7 \u09af\u09a6\u09bf \u0997\u09c1\u09a3\u09ab\u09b2 \u0985\u09ad\u09c7\u09a6 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u09a4\u09ac\u09c7 \u09a4\u09be\u0995\u09c7 \u0987\u0989\u09a8\u09bf\u099f\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964 \u09af\u09a6\u09bf A \u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">k_1A+k_2B<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09c7\u09ae\u09a8: <span class=\"katex-eq\" data-katex-display=\"false\">a=\\frac{1}{\\sqrt{3}}\\begin{bmatrix}\n\n1 &amp; 1+i\\\\\n\n1-i &amp; -1\n\n\\end{bmatrix}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore A^{\\theta}=\\bar{A^T}=\\frac{1}{\\sqrt{3}}\\begin{bmatrix}\n\n1 &amp; 1+i\\\\\n\n1-i &amp; -1\n\n\\end{bmatrix}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">AA^{\\theta}=\\bar{A^T}=\\frac{1}{\\sqrt{3}}\\begin{bmatrix}\n\n1 &amp; 1+i\\\\\n\n1-i &amp; -1\n\n\\end{bmatrix}\\frac{1}{\\sqrt{3}}\\begin{bmatrix}\n\n1 &amp; 1+i\\\\\n\n1-i &amp; -1\n\n\\end{bmatrix}=\\frac{1}{3}\\begin{bmatrix}\n\n3 &amp; 0\\\\\n\n0 &amp; 3\n\n\\end{bmatrix}=\\begin{bmatrix}\n\n1 &amp; 0\\\\\n\n0 &amp; 1\n\n\\end{bmatrix}=I_2<\/span>\n<p><b>Note:\u00a0<\/b><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">AA^{\\theta}=I<\/span> \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">A^{-1}=A^{\\theta}<\/span><\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A \u098f\u09ac\u0982 B \u0989\u09ad\u09af\u09bc\u0987 \u098f\u0995\u0987 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09b2\u09c7 AB \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u0993 \u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A \u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09b2\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">A^{-1}, A^TA<\/span> <\/span><span style=\"font-weight: 400;\">\u0989\u09ad\u09af\u09bc\u0987 \u0987\u0989\u09a8\u09bf\u099f\u09cd\u09af\u09be\u09b0\u09c0 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09ac\u09c7\u0964<\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h2><span style=\"color: #339966;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u0995 (Determinant of Matrix)<\/b><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf \u0995\u09cb\u09a8\u09cb \u09ac\u09b0\u09cd\u0997 A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u0997\u09c1\u09b2\u09cb\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09a0\u09bf\u0995 \u09b0\u09c7\u0996\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u0995 \u09a4\u09c8\u09b0\u09bf \u0995\u09b0\u09be \u09b9\u09df \u09a4\u09ac\u09c7 \u09a4\u09be\u0995\u09c7 \u0989\u0995\u09cd\u09a4 A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u0995 \u09ac\u09be A \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b2\u09c7\u0964 \u0987\u09b9\u09be\u09b2\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left | A \\right |<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09be <\/span><span style=\"font-weight: 400;\">det\u00a0A<\/span><span style=\"font-weight: 400;\"> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n<h3><span style=\"color: #800080;\"><b>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09a8\u09bf\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u0995\u09c7\u09b0 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09cd\u09af (Properties of Matrix Determinant)<\/b><\/span><\/h3>\n<p><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf A \u098f\u09ac\u0982 B \u0989\u09ad\u09af\u09bc\u0987 \u098f\u0995\u0987 \u09ae\u09be\u09a4\u09cd\u09b0\u09be\u09b0 \u09ac\u09b0\u09cd\u0997 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09b9\u09af\u09bc \u09a4\u09ac\u09c7\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">(i) \\left | A^T \\right |=\\left | A \\right |\\\\\n\n(ii) \\left | AB \\right |=\\left | A \\right |\\left | B \\right | \u098f\u09ac\u0982 \\left | BA \\right |=\\left | B \\right |\\left | A \\right |\\\\\n\n(iii) A\\; \u09b2\u09ae\u09cd\u09ac\u09bf\u0995\\; \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\\; \u09b9\u09b2\u09c7\\; \\left | A \\right |= \\pm 1\\\\\n\n(iv) A\\; \u09ac\u09bf\u099c\u09cb\u09a1\u09bc\\; \u0995\u09cd\u09b0\u09ae\u09c7\u09b0\\; \u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae\\; \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\\; \u09b9\u09b2\u09c7\\; \\left | a \\right |=0\\\\\n\n(v) A\\; \u099c\u09cb\u09a1\u09bc\\; \u0995\u09cd\u09b0\u09ae\u09c7\u09b0\\; \u09ac\u09bf\u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09ae\\; \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\\; \u09b9\u09b2\u09c7\\; \\left | a \\right |\\; \u09aa\u09c2\u09b0\u09cd\u09a3\u09ac\u09b0\u09cd\u0997\\; \u09b8\u0982\u0996\u09cd\u09af\u09be\\; \u09b9\u09ac\u09c7\u0964\\\\\n\n(vi) \\left | kA \\right |= k^n \\left | A \\right |\\; \u09af\u09c7\u0996\u09be\u09a8\u09c7\\; k\\; \u09b8\u09cd\u0995\u09c7\u09b2\u09be\u09b0\\; \u098f\u09ac\u0982\\; A\\;\n\n\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0\\; \u0995\u09cd\u09b0\u09ae\\; n\u0964\\\\\n\n(vii) \\left | A^n \\right |= \\left | A \\right |^n \u09af\u09c7\u0996\u09be\u09a8\u09c7 n\u2208N.\\\\\n\n(viii) A = diag \\{a_1, a_2, a_3, .\u2026\u2026 a_? \\} \u09b9\u09b2\u09c7 \\left | A \\right |=a_1, a_2, a_3, .\u2026\u2026 a_n\n\n<\/span>\n<p>&nbsp;<\/p>\n<hr \/>\n<div class=\"x1tlxs6b x1g8br2z x1gn5b1j x230xth x14ctfv x1okitfd x6ikm8r x10wlt62 x1mzt3pk x1y1aw1k xn6708d xwib8y2 x1ye3gou x1n2onr6 x13faqbe x1vjfegm\" role=\"none\">\n<div class=\"\">\n<div class=\"x9f619 x1n2onr6 x1ja2u2z __fb-light-mode\" role=\"none\">\n<p dir=\"auto\" role=\"none\">\n<p class=\"x6prxxf x1fc57z9 x1yc453h x126k92a xzsf02u\" dir=\"auto\" role=\"none\"><em><strong>\u098f\u0987\u099a\u098f\u09b8\u09b8\u09bf \u0993 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09be\u09b0\u09cd\u09a5\u09c0\u09a6\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<\/div>\n<\/div>\n<\/div>\n<ul>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-25-online-batch-2-bangla-english-ict\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a \u09e8.\u09e6 (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-26-online-batch-bangla-english-ict\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ac\u09be\u0982\u09b2\u09be, \u0987\u0982\u09b0\u09c7\u099c\u09bf, \u09a4\u09a5\u09cd\u09af \u0993 \u09af\u09cb\u0997\u09be\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2025-online-batch\/\">HSC 25 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/hsc-2026-online-batch\/\">HSC 26 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09ac\u09cd\u09af\u09be\u099a (\u09ab\u09bf\u099c\u09bf\u0995\u09cd\u09b8, \u0995\u09c7\u09ae\u09bf\u09b8\u09cd\u099f\u09cd\u09b0\u09bf, \u09ae\u09cd\u09af\u09be\u09a5, \u09ac\u09be\u09df\u09cb\u09b2\u099c\u09bf)<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/medical-admission-course\/\">\u09ae\u09c7\u09a1\u09bf\u0995\u09c7\u09b2 \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-a-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/dhaka-university-b-unit-admission-course\/\">\u09a2\u09be\u0995\u09be \u09ad\u09be\u09b0\u09cd\u09b8\u09bf\u099f\u09bf B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/buet-ques-solve\/\">\u09ac\u09c1\u09df\u09c7\u099f \u0995\u09cb\u09b6\u09cd\u099a\u09c7\u09a8 \u09b8\u09b2\u09ad \u0995\u09cb\u09b0\u09cd\u09b8<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-a-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b A Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<li role=\"none\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/gst-b-unit-admission-course\/\">\u0997\u09c1\u099a\u09cd\u099b B Unit \u098f\u09a1\u09ae\u09bf\u09b6\u09a8 \u0995\u09cb\u09b0\u09cd\u09b8 &#8211; \u09e8\u09e6\u09e8\u09ea<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p><em><strong>\u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09b8\u09cd\u0995\u09bf\u09b2 \u09a1\u09c7\u09ad\u09c7\u09b2\u09aa\u09ae\u09c7\u09a8\u09cd\u099f \u0995\u09cb\u09b0\u09cd\u09b8\u09b8\u09ae\u09c2\u09b9\u0983<\/strong><\/em><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/study-abroad-complete-guideline\/\">\u09ac\u09bf\u09a6\u09c7\u09b6\u09c7 \u0989\u099a\u09cd\u099a\u09b6\u09bf\u0995\u09cd\u09b7\u09be: Study Abroad Complete Guideline<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/student-hacks\/\">Student Hacks<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ielts-course\/\">IELTS Course by Munzereen Shahid<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/english-grammar-course\/\">Complete English Grammar Course<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ms-bundle\/\"> Microsoft Office 3 in 1 Bundle<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/ghore-boshe-freelancing\/\">\u0998\u09b0\u09c7 \u09ac\u09b8\u09c7 Freelancing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/facebook-marketing\/\">Facebook Marketing<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/10minuteschool.com\/product\/adobe-4-in-1-bundle\/\">Adobe 4 in 1 Bundle<\/a><\/span><\/li>\n<\/ul>\n<hr \/>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\"><em>\u09e7<\/em><em>\u09e6 \u09ae\u09bf\u09a8\u09bf\u099f \u09b8\u09cd\u0995\u09c1\u09b2\u09c7\u09b0 \u0995\u09cd\u09b2\u09be\u09b8\u0997\u09c1\u09b2\u09cb \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09a4\u09c7 \u09ad\u09bf\u099c\u09bf\u099f: <span style=\"color: #993300;\"><strong><a style=\"color: #993300;\" href=\"https:\/\/10minuteschool.com\/?ref=https%3A%2F%2Fblog.10minuteschool.com%2Fwordpress%2F&amp;post_id=78178&amp;blog_category_id=700\">www.10minuteschool.com<\/a><\/strong><\/span><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 (Matrix) \u0995\u09be\u0995\u09c7 \u09ac\u09b2\u09c7? \u0995\u09a4 \u09aa\u09cd\u09b0\u0995\u09be\u09b0 \u0993 \u0995\u09bf \u0995\u09bf? \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u0995\u09be\u0995\u09c7 \u09ac\u09b2\u09c7? \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8 \u0993 \u0997\u09a3\u09bf\u09a4 \u098f\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09a4\u09a5\u09cd\u09af \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09b8\u09be\u09b0\u09bf (\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u09b0\u09c7\u0996\u09be) \u0993 \u0995\u09b2\u09be\u09ae (\u0989\u09b2\u09ae\u09cd\u09ac \u09b0\u09c7\u0996\u09be) \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u09be\u099c\u09be\u09b2\u09c7 \u09af\u09c7 \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09ac\u09bf\u09a8\u09cd\u09af\u09be\u09b8 (rectangular arrays) \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc \u098f\u0995\u09c7 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8 \u09ac\u09b2\u09c7\u0964 \u09ae\u09cd\u09af\u09be\u099f\u09cd\u09b0\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u09b8\u09be\u09b0\u09bf<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/types-of-matrix\/\">Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3026,4256,3037,50],"tags":[623,625,609,624,612],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/987"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=987"}],"version-history":[{"count":9,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/987\/revisions"}],"predecessor-version":[{"id":16114,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/987\/revisions\/16114"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=987"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=987"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}