{"id":321,"date":"2023-07-06T06:35:36","date_gmt":"2023-07-06T06:35:36","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e8%ae%a1%e7%ae%97%e7%89%b9%e5%be%81%e5%80%bc-%e7%89%b9%e5%be%81%e5%80%bc%e5%92%8c%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f\/"},"modified":"2023-07-06T06:35:36","modified_gmt":"2023-07-06T06:35:36","slug":"%e8%ae%a1%e7%ae%97%e7%89%b9%e5%be%81%e5%80%bc-%e7%89%b9%e5%be%81%e5%80%bc%e5%92%8c%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e8%ae%a1%e7%ae%97%e7%89%b9%e5%be%81%e5%80%bc-%e7%89%b9%e5%be%81%e5%80%bc%e5%92%8c%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f\/","title":{"rendered":"\u77e9\u9635\u7684\u7279\u5f81\u503c\uff08\u6216\u7279\u5f81\u503c\uff09\u548c\u7279\u5f81\u5411\u91cf\uff08\u6216\u7279\u5f81\u5411\u91cf\uff09"},"content":{"rendered":"<p>\u672c\u9875\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u4e5f\u5206\u522b\u79f0\u4e3a\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u6709\u5173\u5982\u4f55\u8ba1\u7b97\u5b83\u4eec\u7684\u793a\u4f8b\u4ee5\u53ca\u7528\u4e8e\u7ec3\u4e60\u7684\u5206\u6b65\u89e3\u51b3\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u4ec0\u4e48\u662f\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff1f<\/h2>\n<p>\u867d\u7136\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u6982\u5ff5\u6bd4\u8f83\u96be\u7406\u89e3\uff0c\u4f46\u5b83\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a <\/p>\n<div style=\"background-color:#dff6ff;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px\" class=\"has-background\">\n<p style=\"text-align:left\"><strong>\u7279\u5f81\u5411\u91cf\u6216\u7279\u5f81\u5411\u91cf<\/strong>\u662f\u7ebf\u6027\u6620\u5c04\u7684\u975e\u96f6\u5411\u91cf\uff0c\u5f53\u7ecf\u8fc7\u7ebf\u6027\u6620\u5c04\u53d8\u6362\u65f6\uff0c\u4f1a\u4ea7\u751f\u5b83\u4eec\u7684\u6807\u91cf\u500d\u6570\uff08\u5b83\u4eec\u4e0d\u6539\u53d8\u65b9\u5411\uff09\u3002\u8be5\u6807\u91cf\u5c31\u662f<strong>\u7279\u5f81\u503c\u6216\u7279\u5f81\u503c<\/strong>\u3002<\/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-710a5e2df8739c35c060f790f5592734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Av = \\lambda v\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"65\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u91d1\u5b50<\/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>\u662f\u7ebf\u6027\u6620\u5c04\u7684\u77e9\u9635\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"v\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u7279\u5f81\u5411\u91cf\u5e76\u4e14<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u81ea\u5df1\u7684\u4ef7\u503c\u3002<\/p>\n<\/div>\n<p>\u7279\u5f81\u503c\u4e5f\u79f0\u4e3a\u7279\u5f81\u503c\u3002\u751a\u81f3\u8fd8\u6709\u6570\u5b66\u5bb6\u7528\u5fb7\u8bed\u8bcd\u6839\u201ceigen\u201d\u6765\u6307\u5b9a\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff1a<em>\u7279\u5f81\u503c<\/em>\u4ee3\u8868\u7279\u5f81\u503c\uff0c<em>\u7279\u5f81\u5411\u91cf<\/em>\u4ee3\u8868\u7279\u5f81\u5411\u91cf\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5982\u4f55\u8ba1\u7b97\u77e9\u9635\u7684\u7279\u5f81\u503c\uff08\u6216\u7279\u5f81\u503c\uff09\u548c\u7279\u5f81\u5411\u91cf\uff08\u6216\u7279\u5f81\u5411\u91cf\uff09\uff1f<\/h2>\n<p>\u8981\u627e\u5230\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u60a8\u5fc5\u987b\u9075\u5faa\u6574\u4e2a\u8fc7\u7a0b\uff1a<\/p>\n<ol style=\"color:#1976d2; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#262626;font-weight: normal;\">\u901a\u8fc7\u6c42\u89e3\u4ee5\u4e0b\u884c\u5217\u5f0f\u8ba1\u7b97\u77e9\u9635\u7684\u7279\u5f81\u65b9\u7a0b\uff1a<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7224fcfc13d25429e22216a3d4124cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:15px\"><span style=\"color:#262626;font-weight: normal;\">\u6211\u4eec\u6c42\u6b65\u9aa41\u4e2d\u5f97\u5230\u7684\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\u3002\u8fd9\u4e9b\u6839\u5c31\u662f\u77e9\u9635\u7684\u7279\u5f81\u503c\u3002<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbe85bd9aff702c72a31d3889f035518_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)=0 \\ \\longrightarrow \\ \\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:15px\"><span style=\"color:#262626;font-weight: normal;\">\u8ba1\u7b97\u6bcf\u4e2a\u7279\u5f81\u503c\u7684\u7279\u5f81\u5411\u91cf\u3002\u4e3a\u6b64\uff0c\u9700\u8981\u5bf9\u6bcf\u4e2a\u7279\u5f81\u503c\u6c42\u89e3\u4ee5\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-372f1009cb2b47f939cf9291f0f23885_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-\\lambda I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/ol>\n<p>\u8fd9\u5c31\u662f\u6c42\u77e9\u9635\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u65b9\u6cd5\uff0c\u4f46\u8fd9\u91cc\u6211\u4eec\u4e5f\u7ed9\u4f60\u4e00\u4e9b\u63d0\u793a\uff1a\ud83d\ude09 <\/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 style=\"text-align:left\"> <strong>Tips<\/strong> \uff1a\u6211\u4eec\u53ef\u4ee5\u5229\u7528\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u6027\u8d28\u6765\u66f4\u5bb9\u6613\u5730\u8ba1\u7b97\u5b83\u4eec\uff1a<\/p>\n<p style=\"text-align:left\"> <strong><span style=\"color:#1976d2;\">\u2713<\/span><\/strong>\u77e9\u9635\u7684\u8ff9\uff08\u4e3b\u5bf9\u89d2\u7ebf\u4e4b\u548c\uff09\u7b49\u4e8e\u6240\u6709\u7279\u5f81\u503c\u4e4b\u548c\u3002<\/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-d4b8ae7f7f7a36be08403ae6ba8b3d32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle tr(A)=\\sum_{i=1}^n \\lambda_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"109\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong><span style=\"color:#1976d2;\">\u2713<\/span><\/strong>\u6240\u6709\u7279\u5f81\u503c\u7684\u4e58\u79ef\u7b49\u4e8e\u77e9\u9635\u7684\u884c\u5217\u5f0f\u3002<\/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-7aa4b68759894e3f25d6475c3b6f71b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle det(A)=\\prod_{i=1}^n \\lambda_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"115\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong><span style=\"color:#1976d2;\">\u2713<\/span><\/strong>\u5982\u679c\u884c\u6216\u5217\u4e4b\u95f4\u5b58\u5728\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u77e9\u9635\u81f3\u5c11\u6709\u4e00\u4e2a\u7279\u5f81\u503c\u7b49\u4e8e0\u3002<\/p>\n<\/div>\n<p>\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u77e9\u9635\u7684\u7279\u5f81\u5411\u91cf\u548c\u7279\u5f81\u503c\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u4f8b\u5b50\uff0c\u4ee5\u4fbf\u66f4\u597d\u5730\u7406\u89e3\u8be5\u65b9\u6cd5\uff1a<\/p>\n<h2 class=\"wp-block-heading\">\u8ba1\u7b97\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u793a\u4f8b\uff1a<\/h2>\n<ul>\n<li>\u6c42\u4ee5\u4e0b\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff1a<\/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-e82dbe4f6e975e1374cab2c1b74638b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}1&amp;0\\\\[1.1ex] 5&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u77e9\u9635\u7684\u7279\u5f81\u65b9\u7a0b\u3002\u4e3a\u6b64\uff0c\u5fc5\u987b\u89e3\u51b3\u4ee5\u4e0b\u51b3\u5b9a\u56e0\u7d20\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-283812fe5eed97f58568fb6e515e3ff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}1- \\lambda &amp;0\\\\[1.1ex] 5&amp;2-\\lambda \\end{vmatrix} = \\lambda^2-3\\lambda +2\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"338\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u8ba1\u7b97\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5f97\u5230\u7684\u7ed3\u679c\u7b49\u4e8e0\u5e76\u6c42\u89e3\u65b9\u7a0b\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-2287061273d7f8502e0dbf1cb2fe1ad7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda^2-3\\lambda +2 = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"122\" style=\"vertical-align: -2px;\"><\/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-fdee5858b8b0187078ea372d9362900f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda= \\cfrac{-(-3)\\pm \\sqrt{(-3)^2-4\\cdot 1 \\cdot 2}}{2\\cdot 1} = \\cfrac{+3\\pm 1}{2}=\\begin{cases} \\lambda = 1 \\\\[2ex] \\lambda = 2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"419\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u65b9\u7a0b\u7684\u89e3\u5c31\u662f\u77e9\u9635\u7684\u7279\u5f81\u503c\u3002<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u6709\u4e86\u7279\u5f81\u503c\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u7279\u5f81\u5411\u91cf\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u6bcf\u4e2a\u7279\u5f81\u503c\u6c42\u89e3\u4ee5\u4e0b\u7cfb\u7edf\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-372f1009cb2b47f939cf9291f0f23885_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-\\lambda I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 1 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-372f1009cb2b47f939cf9291f0f23885_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-\\lambda I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"><\/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-4f0cbd7a7e0670410881dcc0bfd4969c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-1 I)\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"163\" 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-e1f49b7ecec643964e4a14cd17ddecb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}0&amp;0\\\\[1.1ex] 5&amp;1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"156\" 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-06473aeaa487551bca2eb98ff786c8f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 0x+0y = 0 \\\\[2ex] 5x+y = 0\\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"112\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4ece\u8fd9\u4e9b\u65b9\u7a0b\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u5b50\u7a7a\u95f4\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-82da1eb92338b5dc67c9e65188b6c247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=-5x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7279\u5f81\u5411\u91cf\u5b50\u7a7a\u95f4\u4e5f\u79f0\u4e3a\u7279\u5f81\u7a7a\u95f4\u3002<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u5fc5\u987b\u627e\u5230\u8fd9\u4e2a\u5e72\u51c0\u7a7a\u95f4\u7684\u57fa\u6570\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u503c 1 \u8d4b\u7ed9\u53d8\u91cf<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u7279\u5f81\u5411\u91cf\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-f4700ed7bb632b97f0ce1bec12409888_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x = 1 \\ \\longrightarrow \\ y=-5\\cdot 1 = -5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"216\" style=\"vertical-align: -4px;\"><\/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-8af03064a8f197990df832e71472cab0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] -5\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"79\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p>\u6700\u540e\uff0c\u4e00\u65e6\u627e\u5230\u4e0e\u7279\u5f81\u503c 1 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\uff0c\u6211\u4eec\u5c31\u91cd\u590d\u8be5\u8fc7\u7a0b\u6765\u8ba1\u7b97\u7279\u5f81\u503c 2 \u7684\u7279\u5f81\u5411\u91cf\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-372f1009cb2b47f939cf9291f0f23885_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-\\lambda I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"><\/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-3d52ccfc2cbc996d3844af6c699a81b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-2I)\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"163\" 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-24442a53901cc9f0622aecf66ef2dc25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}-1&amp;0\\\\[1.1ex] 5&amp;0\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"169\" 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-fbd3a434bf3f89ed38a893a98befee97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -x+0y = 0 \\\\[2ex] 5x+0y = 0\\end{array}\\right\\} \\longrightarrow \\ x=0\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"207\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ea\u6709\u5411\u91cf\u7684\u7b2c\u4e00\u4e2a\u5206\u91cf\u5fc5\u987b\u4e3a 0\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u7ed9<\/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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002\u4f46\u4e3a\u4e86\u66f4\u5bb9\u6613\uff0c\u6700\u597d\u8f93\u5165 1\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-f47b6a21a448d003d909c0c1c969b8f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}0 \\\\[1.1ex] 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"66\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7efc\u4e0a\uff0c\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-1668ed5f36ad0a8fcb28a264c76b6163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 1 \\qquad v = \\begin{pmatrix}1 \\\\[1.1ex] -5 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"158\" 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-56b0287c0bea71a1e5a258373aaa47d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 2 \\qquad v = \\begin{pmatrix}0 \\\\[1.1ex] 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"144\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u60a8\u77e5\u9053\u5982\u4f55\u627e\u5230\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u60a8\u53ef\u80fd\u4f1a\u60f3\u2026\u2026\u5b83\u4eec\u6709\u4ec0\u4e48\u7528\uff1f\u597d\u5427\uff0c\u4e8b\u5b9e\u8bc1\u660e\u5b83\u4eec\u5bf9\u4e8e<a href=\"https:\/\/mathority.org\/cn\/\u5982\u4f55\u5bf9\u89d2\u5316\u53ef\u5bf9\u89d2\u5316\u77e9\u9635-2x2-3x3-4x4-\u77e9\u9635\u7684\u5bf9\u89d2\u5316\u7ec3\u4e60\u9010\u6b65\u89e3\u51b3\/\">\u77e9\u9635\u5bf9\u89d2\u5316<\/a>\u975e\u5e38\u6709\u7528\uff0c\u4e8b\u5b9e\u4e0a\u8fd9\u662f\u5b83\u4eec\u7684\u4e3b\u8981\u5e94\u7528\u3002\u8981\u4e86\u89e3\u66f4\u591a\u4fe1\u606f\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u67e5\u770b\u5982\u4f55\u4f7f\u7528\u94fe\u63a5\u5bf9\u77e9\u9635\u8fdb\u884c\u5bf9\u89d2\u5316\uff0c\u5176\u4e2d\u9010\u6b65\u89e3\u91ca\u4e86\u8be5\u8fc7\u7a0b\uff0c\u5e76\u4e14\u8fd8\u6709\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u53ef\u4f9b\u7ec3\u4e60\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u5df2\u89e3\u51b3\u7684\u5173\u4e8e\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u7684\u7ec3\u4e60\uff08\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff09<\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b2\u9636\u65b9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-0c6e3869ea2848140f026afc2ff8d554_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}3&amp;1\\\\[1.1ex] 2&amp;4\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" 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\">\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u77e9\u9635\u7684\u884c\u5217\u5f0f\u51cf\u53bb\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684 \u03bb\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-fadce42062bb04b7477318fdc35c4285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}3- \\lambda &amp;1\\\\[1.1ex] 2&amp;4-\\lambda \\end{vmatrix} = \\lambda^2-7\\lambda +10\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"348\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\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-7139127430fa6b78b78715d57a6fdf1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda^2-7\\lambda +10=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda = 2 \\\\[2ex] \\lambda = 5 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"239\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 2 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-1b024c5f7e5acd0be55824c37befc587_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A- 2I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-614f9247b0d79635f70ec79eaa8c6529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}1&amp;1\\\\[1.1ex] 2&amp;2\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"156\" 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-272495fa6e8f89ba4e7c6a6d848cb38a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} x+y = 0 \\\\[2ex] 2x+2y = 0\\end{array}\\right\\} \\longrightarrow \\ x=-y\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"216\" 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-77c240aaa8b75f1e5353c295ee86ad50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"79\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 5 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-f48052a078660236820e9f605996e193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-5I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-b8aa7cae3057d78343128cd1095df24e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}-2&amp;1\\\\[1.1ex] 2&amp;-1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"183\" 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-d8c38e500cf7103b1dc0e91ea1b4531a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -2x+y = 0 \\\\[2ex] 2x-y = 0\\end{array}\\right\\} \\longrightarrow \\ y=2x\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"216\" 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-8be56f81b5aef28783636f85c4dbd643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"66\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-cde889d89562f2e42bd6610b0045c118_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 2 \\qquad v = \\begin{pmatrix}1 \\\\[1.1ex] -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"158\" 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-3e954ba60fdc7eba60ba8530980854c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 5 \\qquad v = \\begin{pmatrix}1\\\\[1.1ex] 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"144\" 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\u4e602<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b2&#215;2\u65b9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-54b0188c9fbadd6c3e35315443b71efd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}2&amp;1\\\\[1.1ex] 3&amp;0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"95\" 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\">\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u77e9\u9635\u7684\u884c\u5217\u5f0f\u51cf\u53bb\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u03bb\uff0c\u5f97\u5230\u7279\u5f81\u65b9\u7a0b\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-88fcd3b21ad2fa5a4d1d7789a86043e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}2- \\lambda &amp;1\\\\[1.1ex] 3&amp;-\\lambda \\end{vmatrix} = \\lambda^2-2\\lambda -3\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u6211\u4eec\u6765\u8ba1\u7b97\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\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-2614817b28bdb25c4fd89d4c773b4e35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda^2-2\\lambda -3=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda = -1 \\\\[2ex] \\lambda = 3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c-1\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-f3e4bb6ba47bb4b9084b8a34d03dd35f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-(-1)I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -5px;\"><\/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-cdddf8c6da3e8066da62f60da7e9c603_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A+1I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-e4b3d926f1a25454c3e645d79b28887d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 3&amp;1\\\\[1.1ex] 3&amp;1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"156\" 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-a7a6529e3ed8eb1607caa88475bcbb8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 3x+1y = 0 \\\\[2ex] 3x+1y = 0\\end{array}\\right\\} \\longrightarrow \\ y=-3x\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"225\" 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-67716508d5a9772f98c3f006f012dff1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"79\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 3 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-50e802072a0f6e2942bc873d6a466909_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-3I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-20e5d0be7e6dbe91bf15c835dac63b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix}-1&amp;1\\\\[1.1ex] 3&amp;-3\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\end{pmatrix} =}\\begin{pmatrix}0 \\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"183\" 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-8355b1ade79ba1508633f309926bc221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -1x+1y = 0 \\\\[2ex] 3x-3y = 0\\end{array}\\right\\} \\longrightarrow \\ y=x\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"216\" 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-0f3cac5769795f1730fcbf118fdfbbc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"66\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-95e2b0bf0405bc0c301600cbb4b2b28a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = -1 \\qquad v = \\begin{pmatrix}1 \\\\[1.1ex] -3 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"172\" 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-6322d97c5d24c1227b06dddf4b0974c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 3 \\qquad v = \\begin{pmatrix}1\\\\[1.1ex] 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"144\" 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>\u786e\u5b9a\u4ee5\u4e0b3\u9636\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-a0e4f4147cbc9e0b657ff432f64bc8e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}1&amp;2&amp;0\\\\[1.1ex] 2&amp;1&amp;0\\\\[1.1ex] 0&amp;1&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" 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\">\u6211\u4eec\u9996\u5148\u8981\u6c42\u89e3\u77e9\u9635A\u51cf\u53bb\u5355\u4f4d\u77e9\u9635\u4e58\u4ee5lambda\u7684\u884c\u5217\u5f0f\uff0c\u5f97\u5230\u7279\u5f81\u65b9\u7a0b\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-0af2ff4694103925883916b6a974c84d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}1-\\lambda&amp;2&amp;0\\\\[1.1ex] 2&amp;1-\\lambda&amp;0\\\\[1.1ex] 0&amp;1&amp;2-\\lambda\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"281\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u884c\u5217\u5f0f\u7684\u6700\u540e\u4e00\u5217\u6709\u4e24\u4e2a\u96f6\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5229\u7528\u8fd9\u4e00\u70b9\u901a\u8fc7\u6b64\u5217\u901a\u8fc7\u8f85\u56e0\u5b50\uff08\u6216\u8865\u6570\uff09\u8ba1\u7b97\u884c\u5217\u5f0f\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-ec7e7a2ec96b8d0721392c28838d105e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix}1-\\lambda&amp;2&amp;0\\\\[1.1ex] 2&amp;1-\\lambda&amp;0\\\\[1.1ex] 0&amp;1&amp;2-\\lambda\\end{vmatrix}&amp; = (2-\\lambda)\\cdot  \\begin{vmatrix}1-\\lambda&amp;2\\\\[1.1ex] 2&amp;1-\\lambda \\end{vmatrix} \\\\[3ex] &amp; = (2-\\lambda)[\\lambda^2 -2\\lambda -3] \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"136\" width=\"364\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u9700\u8981\u8ba1\u7b97\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\u3002\u6700\u597d\u4e0d\u8981\u5c06\u62ec\u53f7\u76f8\u4e58\uff0c\u56e0\u4e3a\u8fd9\u6837\u6211\u4eec\u4f1a\u5f97\u5230\u4e09\u6b21\u591a\u9879\u5f0f\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4e24\u4e2a\u56e0\u5b50\u5206\u522b\u6c42\u89e3\uff0c\u5219\u66f4\u5bb9\u6613\u83b7\u5f97\u7279\u5f81\u503c\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-adbfb1815d4a480c0584dfee1d8039fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (2-\\lambda)[\\lambda^2 -2\\lambda -3]=0 \\ \\longrightarrow \\ \\begin{cases} 2-\\lambda=0 \\ \\longrightarrow \\ \\lambda = 2 \\\\[2ex] \\lambda^2 -2\\lambda -3=0 \\ \\longrightarrow \\begin{cases}\\lambda = -1 \\\\[2ex] \\lambda = 3 \\end{cases} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"489\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 2 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-6c6944f71d79a33d4789affbc82db4c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-2I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-a6a12c460df4d2f44709c4fd595193dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -1&amp;2&amp;0\\\\[1.1ex] 2&amp;-1&amp;0\\\\[1.1ex] 0&amp;1&amp;0\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"216\" 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-5c24e4b7b060a826203e3a049ddfc191_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -x+2y = 0 \\\\[2ex] 2x-y = 0\\\\[2ex] y=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} y=0 \\\\[2ex] x=y=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"248\" 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-75ebf6f61121b67afd80cdcec30a1709_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}0 \\\\[1.1ex] 0 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c-1\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-76cc8bb12c3b49d4964b2b3f661677ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A+I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"99\" style=\"vertical-align: -5px;\"><\/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-d23c4438a53032df27cc5334d4437c18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2&amp;2&amp;0\\\\[1.1ex] 2&amp;2&amp;0\\\\[1.1ex] 0&amp;1&amp;3\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" 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-e023d57d34510e5e8f3a37c20d170e72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 2x+2y = 0 \\\\[2ex] 2x+2y = 0\\\\[2ex] y+3z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=-y \\\\[2ex] y=-3z \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"233\" 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-0be9ef18fb17845818bdd9de51dcb114_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}3 \\\\[1.1ex] -3 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 3 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-50e802072a0f6e2942bc873d6a466909_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-3I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-d0360154b87545dd87e1b0b7bc06f4e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -2&amp;2&amp;0\\\\[1.1ex] 2&amp;-2&amp;0\\\\[1.1ex] 0&amp;1&amp;-1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"229\" 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-b8d514791286e43eae4b09d893d528df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -2x+2y = 0 \\\\[2ex] 2x-2y = 0\\\\[2ex] y-z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=y \\\\[2ex] y=z \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"224\" 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-99f86f65a5a9c69119285377d88f2efa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] 1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-fe42249314c1698847242c608bd65843_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 2 \\qquad v = \\begin{pmatrix}0 \\\\[1.1ex] 0 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"146\" 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-d412e1f81df9d6425db73113aaae5cd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = -1 \\qquad v = \\begin{pmatrix}3 \\\\[1.1ex] -3 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"174\" 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-f581aa37c9698dfb32062777a5a75b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 3 \\qquad v = \\begin{pmatrix}1\\\\[1.1ex] 1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"146\" 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\u4e604<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b3&#215;3\u65b9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-1323184f42d56f070e5b46a75a2e5c4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}2&amp;1&amp;3\\\\[1.1ex]-1&amp;1&amp;1\\\\[1.1ex] 1&amp;2&amp;4\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"136\" 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\">\u6211\u4eec\u9996\u5148\u6c42\u89e3\u77e9\u9635\u7684\u884c\u5217\u5f0f\u51cf\u53bb\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u03bb\uff0c\u5f97\u5230\u7279\u5f81\u65b9\u7a0b\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-bc48c8489b25004ef131cc6ced36b929_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}2-\\lambda&amp;1&amp;3\\\\[1.1ex]-1&amp;1-\\lambda&amp;1\\\\[1.1ex] 1&amp;2&amp;4-\\lambda\\end{vmatrix}=-\\lambda^3+7\\lambda^2-10\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4ece\u7279\u5f81\u591a\u9879\u5f0f\u4e2d\u63d0\u53d6\u4e00\u4e2a\u516c\u56e0\u5b50\uff0c\u5e76\u4ece\u6bcf\u4e2a\u65b9\u7a0b\u4e2d\u6c42\u89e3 \u03bb\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-411dab2f65b426c37f8427d81ef13e97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda(-\\lambda^2+7\\lambda-10)=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda=0\\\\[2ex] -\\lambda^2+7\\lambda-10=0 \\ \\longrightarrow \\begin{cases}\\lambda = 2 \\\\[2ex] \\lambda = 5 \\end{cases} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"481\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 0 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-0e3b04137690f84b723e3ed568e1114a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-0I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-bd7ebe2424c6524d522d5bba16d72d33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2&amp;1&amp;3\\\\[1.1ex]-1&amp;1&amp;1\\\\[1.1ex] 1&amp;2&amp;4\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"202\" 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-12cd10d2dc8afdb7a045beae4946b64d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 2x+y+3z= 0 \\\\[2ex] -x+y+z= 0\\\\[2ex] x+2y+4z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=-\\cfrac{2z}{3} \\\\[4ex] y=-\\cfrac{5z}{3} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"104\" width=\"266\" 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-a34877b285f281c83d7e73fa8eb40b9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}-2 \\\\[1.1ex] -5\\\\[1.1ex] 3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 2 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-6c6944f71d79a33d4789affbc82db4c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-2I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-fbcc697a3be877838fae3507dd3c1b68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 0&amp;1&amp;3\\\\[1.1ex]-1&amp;-1&amp;1\\\\[1.1ex] 1&amp;2&amp;2\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"216\" 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-bb8d470bc7bff9f5d8d5a0245b1e7cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} y+3z = 0 \\\\[2ex] -x-y+z= 0\\\\[2ex] x+2y+2z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} y=-3z \\\\[2ex] x=4z \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"263\" 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-30e589c5ae6b940b901454c296d8342b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}4\\\\[1.1ex] -3 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 5 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-f48052a078660236820e9f605996e193_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-5I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-aaf6f17dedf5eecd1e035b9da59da2c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -3&amp;1&amp;3\\\\[1.1ex]-1&amp;-4&amp;1\\\\[1.1ex] 1&amp;2&amp;-1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"229\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-dca8569528fb4923639dd535e25a0f74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -3x+y+3z = 0 \\\\[2ex] -x-4y+z = 0\\\\[2ex] x+2y-z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=z \\\\[2ex] y=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"255\" 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-308b2f0f597fcc084d8d06d6c45fd3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] 0 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-62d8a98f007b72910fcd79622eda19e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 0 \\qquad v = \\begin{pmatrix}-2 \\\\[1.1ex] -5 \\\\[1.1ex] 3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"160\" 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-ee67e876a46b09430d2d73a653f2d743_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 2 \\qquad v = \\begin{pmatrix}4 \\\\[1.1ex] -3 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"160\" 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-99e4e8b0b837c26991777a294f30d49a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 5 \\qquad v = \\begin{pmatrix}1\\\\[1.1ex] 0 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"146\" 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-119\"><\/div>\n<\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e605<\/h3>\n<p>\u8ba1\u7b97\u4ee5\u4e0b3&#215;3\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-a39253beac54a05e9e84d431daf43362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix}2&amp;2&amp;2\\\\[1.1ex] 1&amp;2&amp;0\\\\[1.1ex] 0&amp;1&amp;3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"122\" 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\">\u6211\u4eec\u9996\u5148\u6c42\u89e3\u77e9\u9635\u7684\u884c\u5217\u5f0f\u51cf\u53bb\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u03bb\uff0c\u5f97\u5230\u7279\u5f81\u65b9\u7a0b\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-9392bbf957bee6c445c64192ae96a2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}2-\\lambda&amp;2&amp;2\\\\[1.1ex] 1&amp;2-\\lambda&amp;0\\\\[1.1ex] 0&amp;1&amp;3-\\lambda\\end{vmatrix}=-\\lambda^3+7\\lambda^2-14\\lambda+8\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"468\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u4f7f\u7528\u9c81\u83f2\u5c3c\u89c4\u5219\u627e\u5230\u7279\u5f81\u591a\u9879\u5f0f\u6216\u6700\u5c0f\u591a\u9879\u5f0f\u7684\u6839\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-152ec29207fec8bdac7dabe9e1fbff31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{array}{r|rrrr} &amp; -1&amp;7&amp;-14&amp;8 \\\\[2ex] 1 &amp; &amp; -1&amp;6&amp;-8 \\\\ \\hline &amp;-1\\vphantom{\\Bigl)}&amp;6&amp;-8&amp;0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u6c42\u5f97\u5230\u7684\u591a\u9879\u5f0f\u7684\u6839\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-b92304d107c097ec5712527929011440_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -\\lambda^2+6\\lambda -8=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda =2 \\\\[2ex] \\lambda = 4 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u77e9\u9635\u7684\u7279\u5f81\u503c\u4e3a\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-05492792022e885b332adb0cbba45a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda=1 \\qquad \\lambda =2 \\qquad \\lambda = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"200\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 1 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-78173073be8dbdcab8a122ade043906d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-1I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-981cc7881e44436326a35a7cc36ad26a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1&amp;2&amp;2\\\\[1.1ex] 1&amp;1&amp;0\\\\[1.1ex] 0&amp;1&amp;2\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" 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-d928870722dec65e8b48f7175d5dd4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} x+2y+2z= 0 \\\\[2ex] x+y= 0\\\\[2ex] y+2z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=-y \\\\[2ex] y=-2z \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"263\" 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-da5ca9263773369d5824688b71a31644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}2 \\\\[1.1ex] -2\\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 2 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-6c6944f71d79a33d4789affbc82db4c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-2I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-b9d1686e2947a9bbe1dc10b373128e1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 0&amp;2&amp;2\\\\[1.1ex] 1&amp;0&amp;0\\\\[1.1ex] 0&amp;1&amp;1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" 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-6000063fd1cc954e119cd5d73d08c405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 2y+2z = 0 \\\\[2ex] x= 0\\\\[2ex] y+z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} y=-z \\\\[2ex] x=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"222\" 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-d47216be7fc08447ac3022a105a086b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}0\\\\[1.1ex] -1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 4 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-0545c0847763140ccc62a58cf4207c6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-4I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-15e38e9899a9e8bb47cfbf10a4f05075_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -2&amp;2&amp;2\\\\[1.1ex] 1&amp;-2&amp;0\\\\[1.1ex] 0&amp;1&amp;-1\\end{pmatrix}\\begin{pmatrix}x \\\\[1.1ex] y \\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"229\" 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-004d61132ba8eeee123d8614432cbce2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -2x+2y+2z = 0 \\\\[2ex] x-2y = 0\\\\[2ex] y-z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} x=2y \\\\[2ex] y=z \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"273\" 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-5871bb6e88776aab87e0239540d43677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}2 \\\\[1.1ex] 1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-f1ea8e2eff0c179b9872da8f6fab2d4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 1 \\qquad v = \\begin{pmatrix}2\\\\[1.1ex] -2 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"160\" 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-edc6fd09f9c6a12b26518a9103cc6610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 2 \\qquad v = \\begin{pmatrix}0 \\\\[1.1ex] -1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"160\" 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-b492e98d771e76e77dc68d2fe2ea92c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 4 \\qquad v = \\begin{pmatrix}2 \\\\[1.1ex] 1 \\\\[1.1ex] 1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"146\" 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\u4e606<\/h3>\n<p>\u6c42\u4ee5\u4e0b4\u00d74\u77e9\u9635\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\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-5cb04190d6f536d33b22265317441144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix}1&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;-1&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;2&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"189\" 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\">\u9996\u5148\u6c42\u89e3\u77e9\u9635\u7684\u884c\u5217\u5f0f\u51cf\u53bb\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u03bb\uff0c\u5f97\u5230\u7279\u5f81\u65b9\u7a0b\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-35cae2dd143d77e22a522b49e8d43f3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A-\\lambda I)= \\begin{vmatrix}1-\\lambda&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;-1-\\lambda&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;2-\\lambda&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;3-\\lambda\\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"352\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u884c\u5217\u5f0f\u7684\u6700\u540e\u4e00\u5217\u9664\u4e00\u4e2a\u5143\u7d20\u5916\u4ec5\u5305\u542b\u96f6\uff0c\u56e0\u6b64\u6211\u4eec\u5c06\u5229\u7528\u8fd9\u4e00\u70b9\u901a\u8fc7\u8be5\u5217\u901a\u8fc7\u8f85\u56e0\u5b50\u8ba1\u7b97\u884c\u5217\u5f0f\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-456b0612b308c03fd1643a5ba0f332e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{aligned} \\begin{vmatrix}1-\\lambda&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;-1-\\lambda&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;2-\\lambda&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;3-\\lambda\\end{vmatrix}&amp; = (3-\\lambda)\\cdot  \\begin{vmatrix}1-\\lambda&amp;0&amp;-1\\\\[1.1ex] 2&amp;-1-\\lambda&amp;-3\\\\[1.1ex] -2&amp;0&amp;2-\\lambda\\end{vmatrix} \\\\[3ex] &amp; = (3-\\lambda)[-\\lambda^3 +2\\lambda^2 +3\\lambda] \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"505\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u73b0\u5728\u5fc5\u987b\u8ba1\u7b97\u7279\u5f81\u591a\u9879\u5f0f\u7684\u6839\u3002\u6700\u597d\u4e0d\u8981\u5c06\u62ec\u53f7\u76f8\u4e58\uff0c\u56e0\u4e3a\u8fd9\u6837\u6211\u4eec\u4f1a\u5f97\u5230\u56db\u6b21\u591a\u9879\u5f0f\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4e24\u4e2a\u56e0\u5b50\u5206\u522b\u6c42\u89e3\uff0c\u5219\u66f4\u5bb9\u6613\u8ba1\u7b97\u7279\u5f81\u503c\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-ef6e59f8631cac087c988004aa512b62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (3-\\lambda)[-\\lambda^3 +2\\lambda^2 +3\\lambda]=0 \\ \\longrightarrow \\ \\begin{cases} 3-\\lambda=0 \\ \\longrightarrow \\ \\lambda = 3 \\\\[2ex] -\\lambda^3 +2\\lambda^2 +3\\lambda =0 \\ \\longrightarrow \\ \\lambda(-\\lambda^2 +2\\lambda +3) =0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"620\" 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-786b2892e7045f117498697407d35552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda(-\\lambda^2 +2\\lambda +3)=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda=0  \\\\[2ex] -\\lambda^2 +2\\lambda +3=0 \\ \\longrightarrow \\ \\begin{cases} \\lambda=-1 \\\\[2ex] \\lambda = 3 \\end{cases}\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"483\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 0 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-0e3b04137690f84b723e3ed568e1114a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-0I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-f43f22947b29779ef456e4ac7a5d66a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;-1&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;2&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;3\\end{pmatrix}\\begin{pmatrix}w \\\\[1.1ex] x \\\\[1.1ex] y\\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\\\[1.1ex] 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"258\" 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-c1d7e96203dceb7288f89ab932532351_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} w-y = 0 \\\\[2ex] 2w-x-3y = 0\\\\[2ex] -2w+2y=0 \\\\[2ex] 3z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} w=y \\\\[2ex] x=-w  \\\\[2ex]z=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"263\" 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-3c4a8b3ef3502a2bf8efd6cc398b5ae6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] -1 \\\\[1.1ex] 1  \\\\[1.1ex]0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c-1\u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-cdddf8c6da3e8066da62f60da7e9c603_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A+1I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-7fbbdceca419f15672da0dcb7c15078c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;0&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;3&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;4\\end{pmatrix}\\begin{pmatrix}w \\\\[1.1ex] x \\\\[1.1ex] y\\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\\\[1.1ex] 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"244\" 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-3ff9a5afa0cefa73985e7ba00c945dac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} 2w-y = 0 \\\\[2ex] 2w-3y = 0\\\\[2ex] -2w+3y=0 \\\\[2ex] 4z=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} y=w=0  \\\\[2ex]z=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"263\" 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-daee73fdcebacce8a5e5f7104ed9c213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}0 \\\\[1.1ex] 1 \\\\[1.1ex] 0  \\\\[1.1ex]0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u4e0e\u7279\u5f81\u503c 3 \u76f8\u5173\u7684\u7279\u5f81\u5411\u91cf\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-50e802072a0f6e2942bc873d6a466909_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (A-3I)v=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -5px;\"><\/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-6493c6019a8b9be3254db2ffeaa19703_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} -2&amp;0&amp;-1&amp;0\\\\[1.1ex] 2&amp;-4&amp;-3&amp;0\\\\[1.1ex] -2&amp;0&amp;-1&amp;0\\\\[1.1ex] 0&amp;0&amp;0&amp;0\\end{pmatrix}\\begin{pmatrix}w \\\\[1.1ex] x \\\\[1.1ex] y\\\\[1.1ex] z \\end{pmatrix} =\\begin{pmatrix}0 \\\\[1.1ex] 0\\\\[1.1ex] 0 \\\\[1.1ex] 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"258\" 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-fbcbd01420d80be317ecbec57010b662_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left.\\begin{array}{l} -2w-y = 0 \\\\[2ex] 2w-4x-3y = 0\\\\[2ex] -2w-y=0 \\\\[2ex] 0=0 \\end{array}\\right\\} \\longrightarrow \\ \\begin{array}{l} y=-2w \\\\[2ex] x=2w  \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"280\" 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-3b70eeb51bea073f058763401adf5240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}1 \\\\[1.1ex] 2 \\\\[1.1ex] -2  \\\\[1.1ex]0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7279\u5f81\u503c 3 \u7684\u91cd\u6570\u7b49\u4e8e 2\uff0c\u56e0\u4e3a\u5b83\u91cd\u590d\u4e86\u4e24\u6b21\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u627e\u5230\u53e6\u4e00\u4e2a\u6ee1\u8db3\u76f8\u540c\u65b9\u7a0b\u7684\u7279\u5f81\u5411\u91cf\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-5dc5fd38503b7683d8a7e3df9da9ee8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle v = \\begin{pmatrix}0 \\\\[1.1ex] 0 \\\\[1.1ex] 0  \\\\[1.1ex]1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u77e9\u9635A\u7684\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u4e3a\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-b8bd7188d1d3ed1abe178d9b5f5bbc0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 0 \\qquad v = \\begin{pmatrix}1 \\\\[1.1ex] -1 \\\\[1.1ex] 1  \\\\[1.1ex]0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"160\" 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-2ea128d2a6e5387bd538ac3d0119b2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = -1 \\qquad v = \\begin{pmatrix}0 \\\\[1.1ex] 1 \\\\[1.1ex] 0  \\\\[1.1ex]0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"160\" 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-22d83a8f13bdb44bf1c23f3c6b963d65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 3 \\qquad v = \\begin{pmatrix}1 \\\\[1.1ex] 2 \\\\[1.1ex] -2  \\\\[1.1ex]0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"160\" 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-65cd815fe71a1c6d8063f0f78e3422a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lambda = 3 \\qquad v = \\begin{pmatrix}0 \\\\[1.1ex] 0 \\\\[1.1ex] 0  \\\\[1.1ex]1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"146\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9875\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u4e5f\u5206\u522b\u79f0\u4e3a\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u6709\u5173\u5982\u4f55\u8ba1\u7b97\u5b83\u4eec\u7684\u793a\u4f8b\u4ee5\u53ca\u7528\u4e8e\u7ec3\u4e60\u7684 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e8%ae%a1%e7%ae%97%e7%89%b9%e5%be%81%e5%80%bc-%e7%89%b9%e5%be%81%e5%80%bc%e5%92%8c%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f-%e7%9f%a9%e9%98%b5%e7%9a%84%e7%89%b9%e5%be%81%e5%90%91%e9%87%8f\/\"> <span class=\"screen-reader-text\">\u77e9\u9635\u7684\u7279\u5f81\u503c\uff08\u6216\u7279\u5f81\u503c\uff09\u548c\u7279\u5f81\u5411\u91cf\uff08\u6216\u7279\u5f81\u5411\u91cf\uff09<\/span> \u67e5\u770b\u5168\u6587 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