{"id":282,"date":"2023-07-06T21:19:23","date_gmt":"2023-07-06T21:19:23","guid":{"rendered":"https:\/\/mathority.org\/cn\/2x2-%e5%92%8c-3x3-%e7%9f%a9%e9%98%b5%e7%9a%84%e5%b9%82%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-06T21:19:23","modified_gmt":"2023-07-06T21:19:23","slug":"2x2-%e5%92%8c-3x3-%e7%9f%a9%e9%98%b5%e7%9a%84%e5%b9%82%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/2x2-%e5%92%8c-3x3-%e7%9f%a9%e9%98%b5%e7%9a%84%e5%b9%82%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u77e9\u9635\u5e42"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97<strong>\u77e9\u9635\u7684\u5e42\u3002<\/strong>\u60a8\u8fd8\u5c06\u627e\u5230\u77e9\u9635\u5e42\u7684\u793a\u4f8b\u548c\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u8fd9\u5c06\u5e2e\u52a9\u60a8\u5b8c\u5168\u7406\u89e3\u5b83\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u77e9\u9635\u7684 n \u6b21\u65b9\u4ee5\u53ca\u5982\u4f55\u6c42\u5b83\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u77e9\u9635\u7684\u5e42\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff1f <\/h2>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\">\u8981\u8ba1\u7b97<strong>\u77e9\u9635 \u7684\u5e42<\/strong>\uff0c\u60a8\u5fc5\u987b\u5c06\u77e9\u9635\u4e0e\u5176\u81ea\u8eab\u76f8\u4e58\uff0c\u6b21\u6570\u4e0e\u6307\u6570\u6240\u793a\u7684\u6b21\u6570\u76f8\u540c\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e77b01db3eabfb211a806dcae2fc5c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^4 = A \\cdot A \\cdot A \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"136\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u8981\u83b7\u5f97\u77e9\u9635\u7684\u5e42\uff0c\u60a8\u9700\u8981\u77e5\u9053\u5982\u4f55\u89e3\u51b3<a href=\"https:\/\/mathority.org\/cn\/2x2-\u548c-3x3-\u77e9\u9635\u7684\u4e58\u6cd5\u793a\u4f8b\u548c\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3\/\">\u77e9\u9635\u4e58\u6cd5<\/a>\u3002\u5426\u5219\u4f60\u65e0\u6cd5\u8ba1\u7b97\u529f\u7387\u77e9\u9635\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u8ba1\u7b97\u77e9\u9635\u5e42\u7684\u793a\u4f8b\uff1a <\/h3>\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-puissances-de-matrices-22.webp\" alt=\"2x2 \u77e9\u9635\u7684\u5e42\u793a\u4f8b\" width=\"560\" height=\"471\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u65b9\u9635\u7684\u5e42\u662f\u901a\u8fc7\u77e9\u9635\u4e58\u4ee5\u81ea\u8eab\u6765\u8ba1\u7b97\u7684\u3002\u7c7b\u4f3c\u5730\uff0c\u7acb\u65b9\u77e9\u9635\u7b49\u4e8e\u77e9\u9635\u672c\u8eab\u7684\u5e73\u65b9\u77e9\u9635\u3002\u7c7b\u4f3c\u5730\uff0c\u8981\u6c42\u77e9\u9635\u56db\u6b21\u65b9\u7684\u5e42\uff0c\u5fc5\u987b\u5c06\u77e9\u9635\u4e09\u6b21\u65b9\u4e58\u4ee5\u77e9\u9635\u672c\u8eab\u3002\u7b49\u7b49\u3002<\/p>\n<p>\u60a8\u5e94\u8be5\u77e5\u9053\u77e9\u9635\u5e42\u7684\u4e00\u4e2a\u91cd\u8981\u5c5e\u6027\uff1a<strong>\u53ea\u6709\u5f53\u77e9\u9635\u4e3a\u65b9\u9635\u65f6\uff08\u5373\u884c\u6570\u4e0e\u5217\u6570\u76f8\u540c\u65f6\uff09\u624d\u80fd\u8ba1\u7b97\u77e9\u9635\u7684\u5e42<\/strong>\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u77e9\u9635\u7684n\u6b21\u65b9\u662f\u591a\u5c11\uff1f<\/h2>\n<p><strong>\u77e9\u9635\u7684n\u6b21\u65b9<\/strong>\u662f\u4e00\u4e2a\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u8ba9\u6211\u4eec\u8f7b\u677e\u8ba1\u7b97\u77e9\u9635\u7684\u4efb\u610f\u6b21\u65b9\u3002<\/p>\n<p>\u77e9\u9635\u7684\u5e42\u901a\u5e38\u9075\u5faa\u67d0\u79cd<strong>\u6a21\u5f0f<\/strong>\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u80fd\u591f\u7834\u8bd1\u5b83\u4eec\u9075\u5faa\u7684\u5e8f\u5217\uff0c\u6211\u4eec\u5c06\u80fd\u591f\u8ba1\u7b97\u4efb\u4f55\u5e42\uff0c\u800c\u4e0d\u5fc5\u8fdb\u884c\u6240\u6709\u4e58\u6cd5\u3002<\/p>\n<p>\u8fd9\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u4e00\u4e2a\u516c\u5f0f\u6765\u8ba1\u7b97\u77e9\u9635\u7684 n \u6b21\u65b9\uff0c\u800c\u65e0\u9700\u8ba1\u7b97\u6240\u6709\u6b21\u65b9\u3002 <\/p>\n<div style=\"background-color:#fffde7;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p align=\"LEFT\">\u53d1\u73b0\u6743\u529b\u6240\u9075\u5faa\u7684\u6a21\u5f0f\u7684<strong>\u63d0\u793a<\/strong>\uff1a<\/p>\n<ul style=\"color:#1976d2; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#000000;font-weight: normal;\"><strong>\u6307\u6570\u7684\u5947\u5076\u6027<\/strong>\u3002\u5076\u6b21\u5e42\u53ef\u80fd\u662f\u4e00\u79cd\u65b9\u5f0f\uff0c\u5947\u6b21\u5e42\u662f\u53e6\u4e00\u79cd\u65b9\u5f0f\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px;\"><span style=\"color:#000000;font-weight: normal;\"><strong>\u6807\u5fd7\u7684\u53d8\u5316\u3002<\/strong>\u4f8b\u5982\uff0c\u5076\u6570\u6b21\u65b9\u7684\u5143\u7d20\u53ef\u80fd\u4e3a\u6b63\uff0c\u800c\u5947\u6570\u6b21\u65b9\u7684\u5143\u7d20\u53ef\u80fd\u4e3a\u8d1f\uff0c\u6216\u8005\u53cd\u4e4b\u4ea6\u7136\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px;\"><span style=\"color:#000000;font-weight: normal;\"><strong>\u91cd\u590d\uff1a<\/strong>\u540c\u4e00\u77e9\u9635\u662f\u5426\u6bcf\u9694\u4e00\u5b9a\u6b21\u6570\u7684\u5e42\u91cd\u590d\u4e00\u6b21\u3002<\/span><\/li>\n<li><span style=\"color:#000000;font-weight: normal;\">\u6211\u4eec\u8fd8\u5fc5\u987b\u770b\u770b\u6307\u6570\u548c\u77e9\u9635\u5143\u7d20\u4e4b\u95f4\u662f\u5426\u5b58\u5728<strong>\u5173\u7cfb<\/strong>\u3002<\/span> <\/li>\n<\/ul>\n<\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\">\u8ba1\u7b97\u77e9\u9635 n \u6b21\u65b9\u7684\u793a\u4f8b\uff1a<\/h3>\n<ul>\n<li>\u662f\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0b\u9762\u7684\u77e9\u9635\uff0c\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34564dd93ab535fd300f9ac993829376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^n\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-52b77e64505e02204c8e501aea82c251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{100}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-60016ce1c6799c93007526681fbf4894_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  A = \\begin{pmatrix} 1 &amp; 1 \\\\[1.1ex] 1 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u77e9\u9635\u7684\u51e0\u6b21\u5e42<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u5c1d\u8bd5\u731c\u6d4b\u5e42\u6240\u9075\u5faa\u7684\u6a21\u5f0f\u3002\u6240\u4ee5\u6211\u4eec\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b49aeb7162689d03dd9f9470a2ae1a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07e0009cbaebcb5501371dd9f6795f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ccb300f7879fa598883dafb53bf7a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^4\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2ce79bf092ea6898cbcbc086729ba93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^5:\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-pas-a-pas-des-puissances-des-matrices-22.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3 2x2 \u77e9\u9635\u7684\u5e42\" width=\"409\" height=\"361\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u5f53\u8ba1\u7b97\u81f3<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d1e5d53cda856213bbb6b5796706dd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u6211\u4eec\u770b\u5230\u77e9\u9635\u7684\u5e42<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5b83\u4eec\u9075\u5faa\u4e00\u4e2a\u6a21\u5f0f\uff1a\u6bcf\u6b21\u5e42\u589e\u52a0\uff0c\u7ed3\u679c\u90fd\u4f1a\u4e58\u4ee5 2\u3002\u56e0\u6b64\uff0c<strong>\u6240\u6709\u77e9\u9635\u90fd\u662f 2 \u7684\u5e42\uff1a<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ec7ee835cf9eda6a4f9d497e8baff79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= \\begin{pmatrix} 2 &amp; 2 \\\\[1.1ex] 2 &amp; 2 \\end{pmatrix} =\\begin{pmatrix} 2^1 &amp; 2^1 \\\\[1.1ex] 2^1 &amp; 2^1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"204\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-69c6ff0f4de92192584dadc4719167c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= \\begin{pmatrix} 4 &amp; 4 \\\\[1.1ex] 4 &amp; 4 \\end{pmatrix}=\\begin{pmatrix} 2^2 &amp; 2^2 \\\\[1.1ex] 2^2 &amp; 2^2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"204\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f724a50b220b3026d53e40ee17870359_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= \\begin{pmatrix} 8 &amp; 8 \\\\[1.1ex] 8 &amp; 8 \\end{pmatrix}=\\begin{pmatrix} 2^3 &amp; 2^3 \\\\[1.1ex] 2^3 &amp; 2^3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"204\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5f08f7cc00465a6a098ce7d752aa66f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= \\begin{pmatrix} 16 &amp; 16 \\\\[1.1ex] 16 &amp; 16 \\end{pmatrix}=\\begin{pmatrix} 2^4 &amp; 2^4 \\\\[1.1ex] 2^4 &amp; 2^4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u77e9\u9635<strong>n\u6b21\u65b9<\/strong>\u7684\u516c\u5f0f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944477c7f7578892a57aa3b7c7dd8268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A:\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/nieme-puissance-dune-matrice.webp\" alt=\"2x2 \u77e9\u9635\u7684 n \u6b21\u65b9\" width=\"201\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4ece\u8fd9\u4e2a\u516c\u5f0f\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-560982f344534dee89eb7afbf6be520e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{100}:\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<figure class=\"wp-block-image aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-de-puissance-resolu-dune-matrice.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u6c42\u89e3 2x2 \u77e9\u9635\u7684\u5e42\" width=\"187\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\">\u89e3\u51b3\u4e86\u77e9\u9635\u529f\u7387\u95ee\u9898<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8003\u8651\u4ee5\u4e0b\u7ef4\u5ea6\u4e3a 2\u00d72 \u7684\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdf81cf9fb956a144c7bda96a84ec7db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] -1 &amp; 1  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2589110bbf0eae4fa44ef48ab7b0f416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u77e9\u9635\u7684\u5e42\uff0c\u5fc5\u987b\u5c06\u77e9\u9635\u4e00\u4e58\u4e00\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7581934ef6136b2b48380f1a53c7809_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2 :\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-24916b0b0e4431b0a2ee2b09875dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= A \\cdot A = \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] -1 &amp; 1 \\end{pmatrix} \\cdot \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] -1 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} -1 &amp; 4 \\\\[1.1ex] -2 &amp;  -1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"381\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fecf45671ed5e89f1f756fd265fcf13b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3 :\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-57f79bd420c0044c84a64b431035b8ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= A^2 \\cdot A = \\begin{pmatrix} -1 &amp; 4 \\\\[1.1ex] -2 &amp;  -1 \\end{pmatrix} \\cdot \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] -1 &amp; 1 \\end{pmatrix} =\\begin{pmatrix} -5 &amp; 2 \\\\[1.1ex] -1 &amp;  -5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"403\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u6211\u4eec\u8ba1\u7b97<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f95589f39821fada84cb5b3d4ba91a46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4 :\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bbc2ad8229ee141b323c9bbcc9df00fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= A^3 \\cdot A = \\begin{pmatrix} -5 &amp; 2 \\\\[1.1ex] -1 &amp;  -5 \\end{pmatrix} \\cdot \\begin{pmatrix} 1 &amp; 2 \\\\[1.1ex] -1 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} \\bm{-7} &amp; \\bm{-8} \\\\[1.1ex] \\bm{4} &amp;  \\bm{-7} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"403\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u8003\u8651\u4ee5\u4e0b 2 \u9636\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33db03560b5c28f45eef9aa293484603_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3  \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f350af4394f9224a8a2d726ed6ed0aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{35}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f350af4394f9224a8a2d726ed6ed0aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{35}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7684\u5e42\u592a\u5927\u800c\u65e0\u6cd5\u624b\u52a8\u8ba1\u7b97\uff0c\u56e0\u6b64\u77e9\u9635\u5e42\u5fc5\u987b\u9075\u5faa\u67d0\u79cd\u6a21\u5f0f\u3002\u90a3\u4e48\u6211\u4eec\u6765\u8ba1\u7b97\u4e00\u4e0b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0678e990fe5d8fe1614d53eb51816f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c1d\u8bd5\u7406\u89e3\u5b83\u4eec\u9075\u5faa\u7684\u987a\u5e8f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cb9646cc984d754d2a618e6223e93cd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= A \\cdot A = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 9 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"326\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22fdee28399b9115de98a214ba0c8473_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= A^2 \\cdot A = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 9 \\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 27 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"343\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1a085a2338ce1e74885ca04bbd0011a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= A^3 \\cdot A = \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 27 \\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 81 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"351\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3dc357146829da8323a0755fa16a8ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= A^4 \\cdot A = \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 81 \\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 243 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"360\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u770b\u5230\u5e42\u9075\u5faa\u7684\u6a21\u5f0f\uff1a\u5728\u6bcf\u4e2a\u5e42\u4e0a\uff0c\u9664\u4e86\u7b2c\u4e8c\u884c\u7b2c\u4e8c\u5217\u4e2d\u7684\u5143\u7d20\u4e58\u4ee5 3 \u4e4b\u5916\uff0c\u6240\u6709\u6570\u5b57\u90fd\u4fdd\u6301\u76f8\u540c\u3002\u56e0\u6b64\uff0c<strong>\u6240\u6709\u6570\u5b57\u59cb\u7ec8\u4fdd\u6301\u76f8\u540c\u3002\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u662f 3 \u7684\u5e42\uff1a<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a0bfa34768808832e0fd5d3f730eb27b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3 \\end{pmatrix}=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"188\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f6e007f5ad5d38fd887d39f00bd2b9fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 9 \\end{pmatrix}=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"196\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-585d8a00f418b50f60b4f95d87c5839c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 27 \\end{pmatrix}=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dec6b9db4b59d9759adf85cee442cca3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 81 \\end{pmatrix}=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7244b46950df4d9107cbdb7ad004e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 243 \\end{pmatrix}=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"214\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5<strong>\u77e9\u9635\u7684n\u6b21\u65b9<\/strong>\u516c\u5f0f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e1c\u65b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-beec2f1ed3e47902de0f25fe1901e294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^n=\\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 3^n\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"113\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4ece\u8fd9\u4e2a\u516c\u5f0f\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c4057ee894404b505d020a186733732e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{35}:\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"37\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa3261646ca7bfa41f8ad46331a0af4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\bm{A^{35}=}\\begin{pmatrix} \\bm{1} &amp; \\bm{0} \\\\[1.1ex] \\bm{0} &amp; \\bm{3^{35}}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u8003\u8651\u4ee5\u4e0b 3\u00d73 \u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f11fe8a7dcd1e308faa0af24eee3f362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"126\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a99c928415cd39eb81240e79778e41df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{100}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a99c928415cd39eb81240e79778e41df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{100}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"34\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7684\u5e42\u592a\u5927\u800c\u65e0\u6cd5\u624b\u52a8\u8ba1\u7b97\uff0c\u56e0\u6b64\u77e9\u9635\u5e42\u5fc5\u987b\u9075\u5faa\u67d0\u79cd\u6a21\u5f0f\u3002\u90a3\u4e48\u6211\u4eec\u6765\u8ba1\u7b97\u4e00\u4e0b<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0678e990fe5d8fe1614d53eb51816f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c1d\u8bd5\u7406\u89e3\u5b83\u4eec\u9075\u5faa\u7684\u987a\u5e8f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acb15d7f461d11e3668bc0b96a1fdc06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= A \\cdot A = \\begin{pmatrix} 1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix} =  \\begin{pmatrix} 1 &amp; \\frac{2}{5}   &amp; \\frac{2}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"421\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f416625ded948830fa80799249c12608_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= A^2 \\cdot A = \\begin{pmatrix} 1 &amp; \\frac{2}{5}   &amp; \\frac{2}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1\\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; \\frac{3}{5}   &amp; \\frac{3}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a76fd60051b157f06c2a731ff575d1e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= A^3 \\cdot A = \\begin{pmatrix} 1 &amp; \\frac{3}{5}   &amp; \\frac{3}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1\\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix} =  \\begin{pmatrix} 1 &amp; \\frac{4}{5}   &amp; \\frac{4}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3409c7b8d82ffd21cc084a12405fce74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= A^4 \\cdot A = \\begin{pmatrix} 1 &amp; \\frac{4}{5}   &amp; \\frac{4}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1\\end{pmatrix} \\cdot \\begin{pmatrix}1 &amp; \\frac{1}{5}  &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix} =  \\begin{pmatrix} 1 &amp; \\frac{5}{5}   &amp; \\frac{5}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"429\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u770b\u5230\u5e42\u9075\u5faa\u7684\u6a21\u5f0f\uff1a\u5728\u6bcf\u4e2a\u5e42\u4e0a\uff0c\u6240\u6709\u6570\u5b57\u90fd\u4fdd\u6301\u4e0d\u53d8\uff0c\u9664\u4e86\u5206\u6570\uff0c<strong>\u5206\u5b50\u4e2d\u7684\u5206\u6570\u589e\u52a0\u4e00\uff1a<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-86c72aa2b21e7a68bbebfe7af5daa420_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 1 &amp; \\frac{1}{5}   &amp; \\frac{1}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"126\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ce805455e49bf018f8f22588391ac44c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= \\begin{pmatrix} 1 &amp; \\frac{2}{5}   &amp; \\frac{2}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd5468ece9001274493687f3786b0af3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= \\begin{pmatrix} 1 &amp; \\frac{3}{5}   &amp; \\frac{3}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-07fd0e03c0163b58fffbe0235009fd8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= \\begin{pmatrix} 1 &amp; \\frac{4}{5}   &amp; \\frac{4}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5ea88723757d1f2d8d6de1ac2d3843c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= \\begin{pmatrix} 1 &amp; \\frac{5}{5}   &amp; \\frac{5}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"134\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5<strong><strong>\u7b2cn\u4e2a<\/strong>\u77e9\u9635\u7684\u5e42<\/strong>\u516c\u5f0f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-36386dbc4f20fb573357a406ce713887_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e1c\u65b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56308ff348d67ba1aba5816d85e9ee1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^n= \\begin{pmatrix} 1 &amp; \\frac{n}{5}   &amp; \\frac{n}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4ece\u8fd9\u4e2a\u516c\u5f0f\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u51fa<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d22628ae2f8152f9817b84fa09c97d6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{100}:\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5352f021f5ab30e999c57f978ff55ad6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{100}=   \\begin{pmatrix} 1 &amp; \\frac{100}{5}   &amp; \\frac{100}{5} \\\\[1.1ex] 0 &amp; 1  &amp; 0 \\\\[1.1ex] 0 &amp; 0  &amp; 1 \\end{pmatrix}= \\begin{pmatrix} \\bm{1} &amp; \\bm{20}   &amp; \\bm{20} \\\\[1.1ex] \\bm{0} &amp; \\bm{1}  &amp; \\bm{0} \\\\[1.1ex] \\bm{0} &amp; \\bm{0}  &amp; \\bm{1} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"307\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u8003\u8651\u4ee5\u4e0b\u5927\u5c0f\u4e3a 2\u00d72 \u7684\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4609248b534d656aa9495b58f42e343f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"109\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f8edde6fcaa57b102140f3d4437f95b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f8edde6fcaa57b102140f3d4437f95b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7684\u5e42\u592a\u5927\u800c\u65e0\u6cd5\u624b\u52a8\u8ba1\u7b97\uff0c\u56e0\u6b64\u77e9\u9635\u5e42\u5fc5\u987b\u9075\u5faa\u67d0\u79cd\u6a21\u5f0f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9700\u8981\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f4a7b26a48a1e57dc08ef4c8c662af6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{8}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u4e86\u77e5\u9053\u5b83\u4eec\u9075\u5faa\u7684\u987a\u5e8f\uff1a <\/p>\n<p class=\"has-text-align-center\">\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9a1fb4cf8bb75cf02d76a26054e6bfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= A \\cdot A = \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"381\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-110c4b30c78811cafdd4234e128ed414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= A^2 \\cdot A = \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 0 &amp; 1 \\\\[1.1ex] -1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b1976bbdf3c1daa9d75497efc07975c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= A^3 \\cdot A = \\begin{pmatrix}0 &amp; 1 \\\\[1.1ex] -1 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix} = \\bm{I}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"398\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0266d832a2fc0a04c9f6582dc231d57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= A^4 \\cdot A = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1\\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"361\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-21dea9844b7bfdb990bbb2bc955c866e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^6= A^5 \\cdot A = \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-788e75a71c1dfe4a60f0e52960715efe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^7= A^6 \\cdot A = \\begin{pmatrix} -1 &amp; 0 \\\\[1.1ex] 0 &amp; -1 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 0 &amp; 1 \\\\[1.1ex] -1 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4947286a163847383e3735a508b0037d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^8= A^7 \\cdot A = \\begin{pmatrix}0 &amp; 1 \\\\[1.1ex] -1 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 0 &amp; -1 \\\\[1.1ex] 1 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 \\\\[1.1ex] 0 &amp; 1 \\end{pmatrix} = \\bm{I}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"398\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u901a\u8fc7\u8fd9\u4e9b\u8ba1\u7b97\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6bcf 4 \u6b21\u65b9\u6211\u4eec\u5c31\u5f97\u5230\u5355\u4f4d\u77e9\u9635\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4f1a\u7ed9\u6211\u4eec\u7ed3\u679c\u7684\u5e42\u5355\u4f4d\u77e9\u9635<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2589110bbf0eae4fa44ef48ab7b0f416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b6df3f4d3068241a434e489e7f1d655e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^8\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d390d2dcb2acd63a2b3af76fa1451d29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-26e32d520eee6a2f5c39f1d6de0c9ffc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{16}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,&#8230;\u6240\u4ee5\u8981\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f8edde6fcaa57b102140f3d4437f95b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6211\u4eec\u5fc5\u987b\u5c06 201 \u5206\u89e3\u4e3a 4 \u7684\u500d\u6570\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-etape-par-etape-puissance-dune-matrice.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u6c42\u89e3 2x2 \u77e9\u9635\u7684\u5e42\u548c n \u6b21\u5e42\" class=\"wp-image-327\" width=\"416\" height=\"160\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3c705236856598d218f071b1ca9a370d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 201= 4 \\cdot 50 +1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"119\" style=\"vertical-align: -2px;\"><\/p>\n<p> \uff0c\u7136\u800c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01a8a8f62467b5a911593c44559f2dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{201}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c06\u4f1a\u662f50\u6b21<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1483b12f3e81520e751acccec37f9c21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd8\u6709\u4e00\u6b21<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3937de4ff8cc137d41d4ac1bbccf561c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{1}:\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e169084d9ac06e6c2895a2b1f4be3f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}=\\left(A^4 \\right)^{50} \\cdot A^1\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"142\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u600e\u4e48\u77e5\u9053<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2589110bbf0eae4fa44ef48ab7b0f416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5355\u4f4d\u77e9\u9635<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-867357beec26a26d9d9b4af01b8086e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3f630d4fa8da50f18be6835617a6982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4 =I\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-29c53c0280332f200d37936b211faf39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}=\\left(A^4 \\right)^{50} \\cdot A^1 = I^{50}\\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"217\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b64\u5916\uff0c\u5c06\u5355\u4f4d\u77e9\u9635\u63d0\u5347\u5230\u4efb\u610f\u6570\u5373\u53ef\u5f97\u5230\u5355\u4f4d\u77e9\u9635\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0748e850cbae2f5a2d9eb797e27641b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}= I^{50}\\cdot A = I \\cdot A\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4efb\u4f55\u77e9\u9635\u4e58\u4ee5\u5355\u4f4d\u77e9\u9635\u90fd\u4f1a\u5f97\u5230\u76f8\u540c\u7684\u77e9\u9635\u3002\u6240\u4ee5\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c88ebfbbdcc01a0cbdcf840aba32313e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}= I \\cdot A = A\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"130\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4ec0\u4e48<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01a8a8f62467b5a911593c44559f2dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{201}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u7b49\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-944477c7f7578892a57aa3b7c7dd8268_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A:\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1214abe876a5aede8fbbce79009d5dbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{201}= A =\\begin{pmatrix} \\bm{0} &amp; \\bm{-1} \\\\[1.1ex] \\bm{1} &amp; \\bm{0} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u8003\u8651\u4ee5\u4e0b 3 \u9636\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b8f3ba8b2d15b622f99774be05aa2620_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"164\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8ba1\u7b97\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd886e003dc8d850cca00cfe4d00ed4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u663e\u7136\uff0c\u8ba1\u7b97\u77e9\u9635\u7684\u5e42<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd886e003dc8d850cca00cfe4d00ed4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u592a\u5927\u7684\u8ba1\u7b97\uff0c\u65e0\u6cd5\u624b\u52a8\u5b8c\u6210\uff0c\u56e0\u6b64\u77e9\u9635\u5e42\u5fc5\u987b\u9075\u5faa\u67d0\u79cd\u6a21\u5f0f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9700\u8981\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9dcf97a16a30b4167b19a2313ee060c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e3a\u4e86\u77e5\u9053\u5b83\u4eec\u9075\u5faa\u7684\u987a\u5e8f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4032b55d68a5615911a5b7c997b05e6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^2= A \\cdot A = \\begin{pmatrix}3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 3 &amp; 3 &amp; 1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; 1 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"534\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8b5deef2a7728c5e82e1a1dafb1a939c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3= A^2 \\cdot A = \\begin{pmatrix}3 &amp; 3 &amp; 1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; 1 &amp; -1\\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"500\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f62e856d037138b2ead39b17ccebf96d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^4= A^3 \\cdot A = \\begin{pmatrix}1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"500\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-854da5c09b6662da46acb790afb6d01a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^5= A^4 \\cdot A = \\begin{pmatrix}3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 3 &amp; 3 &amp; 1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; 1 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"541\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c9f804a1c129e18d105fb92254c971fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^6= A^5 \\cdot A = \\begin{pmatrix}3 &amp; 3 &amp; 1 \\\\[1.1ex] -2 &amp; -2 &amp; -1 \\\\[1.1ex] 0 &amp; 1 &amp; -1\\end{pmatrix} \\cdot \\begin{pmatrix} 3 &amp; 4 &amp; -1 \\\\[1.1ex] -2 &amp; -3 &amp; 1 \\\\[1.1ex] -2 &amp; -3 &amp; 0 \\end{pmatrix} = \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"500\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u901a\u8fc7\u8fd9\u4e9b\u8ba1\u7b97\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6bcf 3 \u6b21\u65b9\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u5355\u4f4d\u77e9\u9635\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b83\u4f1a\u7ed9\u6211\u4eec\u7ed3\u679c\u7684\u5e42\u5355\u4f4d\u77e9\u9635<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca00633b1d21d63a177e78aed3846413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-33a1b80dd4db27f09aa071e4b8bf01a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c2f4eb36ca05968a81ef76d76e9275c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{9}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d390d2dcb2acd63a2b3af76fa1451d29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{12}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,&#8230;\u4ee5\u4fbf\u8ba1\u7b97<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd886e003dc8d850cca00cfe4d00ed4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6211\u4eec\u5fc5\u987b\u5c06 62 \u5206\u89e3\u4e3a 3 \u7684\u500d\u6570\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-des-puissances-des-matrices-33.webp\" alt=\"\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3 3x3 \u77e9\u9635\u7684 n \u6b21\u65b9\" class=\"wp-image-339\" width=\"394\" height=\"160\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f1ebd498146526b26797fc73174c6bef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 62= 3 \\cdot 20 +2\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"110\" style=\"vertical-align: -2px;\"><\/p>\n<p> \uff0c\u7136\u800c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bd886e003dc8d850cca00cfe4d00ed4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c06\u4f1a\u662f20\u6b21<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6129a88e40a1a7fa3b922c8ef6ec57cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u8fd8\u6709\u4e00\u6b21<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-490432e07ef01473684f6a975567a3d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{2}:\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"30\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-db1749b0c96e2613326aa9bac2cbf651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}=\\left(A^3 \\right)^{20} \\cdot A^2\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"136\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u6211\u4eec\u600e\u4e48\u77e5\u9053<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca00633b1d21d63a177e78aed3846413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5355\u4f4d\u77e9\u9635<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-867357beec26a26d9d9b4af01b8086e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle I :\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e4af75581d64edceeaa20edefbde7d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^3 =I\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c885875cfd8f37ead41f1b9cae94a3f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}=\\left(A^3 \\right)^{20} \\cdot A^2 = I^{20}\\cdot A^2\" title=\"Rendered by QuickLaTeX.com\" height=\"27\" width=\"217\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b64\u5916\uff0c\u5c06\u5355\u4f4d\u77e9\u9635\u63d0\u5347\u5230\u4efb\u610f\u6570\u5373\u53ef\u5f97\u5230\u5355\u4f4d\u77e9\u9635\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a3175b230605c5218a3fc03c53cbd14b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}= I^{20}\\cdot A^2 = I \\cdot A^2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u4efb\u4f55\u77e9\u9635\u4e58\u4ee5\u5355\u4f4d\u77e9\u9635\u90fd\u4f1a\u5f97\u5230\u76f8\u540c\u7684\u77e9\u9635\u3002\u7136\u800c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-269a862d24453f1dff22c4599b6fa775_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}= I \\cdot A^2 = A^2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4ec0\u4e48<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23af6c06fb07a3267b3401415f6c0449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{62}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u5c06\u7b49\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e1844da717e117a743161ee5e453ae3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"20\" style=\"vertical-align: 0px;\"><\/p>\n<p>\uff0c\u6211\u4eec\u4e4b\u524d\u8ba1\u7b97\u8fc7\u7684\u7ed3\u679c\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f95e17aacde501ca1c28dbf14324f0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^{62}= A^2=\\begin{pmatrix} \\bm{3} &amp; \\bm{3} &amp; \\bm{1} \\\\[1.1ex] \\bm{-2} &amp; \\bm{-2} &amp; \\bm{-1} \\\\[1.1ex] \\bm{0} &amp; \\bm{1} &amp; \\bm{-1} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"223\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u5982\u679c\u8fd9\u4e9b\u5173\u4e8e\u65b9\u9635\u5e42\u7684\u7ec3\u4e60\u5bf9\u60a8\u6709\u7528\uff0c\u60a8\u8fd8\u53ef\u4ee5\u627e\u5230\u5173\u4e8e<a href=\"https:\/\/mathority.org\/cn\/\u77e9\u9635\u52a0\u51cf\u6cd5-2x2-3x3-\u793a\u4f8b\u5df2\u89e3\u51b3\u7ec3\u4e60\/\">\u77e9\u9635\u52a0\u6cd5\u548c\u51cf\u6cd5\uff08\u6700\u5e38\u7528\u7684\u77e9\u9635\u8fd0\u7b97\u4e4b\u4e00\uff09\u7684<\/a>\u5df2\u89e3\u51b3\u5206\u6b65\u7ec3\u4e60\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u77e9\u9635\u7684\u5e42\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u77e9\u9635\u5e42\u7684\u793a\u4f8b\u548c\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u8fd9\u5c06\u5e2e\u52a9\u60a8\u5b8c\u5168\u7406\u89e3\u5b83\u3002\u60a8\u8fd8\u5c06\u4e86\u89e3 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/2x2-%e5%92%8c-3x3-%e7%9f%a9%e9%98%b5%e7%9a%84%e5%b9%82%e7%a4%ba%e4%be%8b%e5%92%8c%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%9a%84%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u77e9\u9635\u5e42<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[7],"tags":[],"class_list":["post-282","post","type-post","status-publish","format-standard","hentry","category-7"],"yoast_head":"<!-- This site is optimized 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