{"id":69,"date":"2023-09-16T13:05:25","date_gmt":"2023-09-16T13:05:25","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e7%8b%ac%e7%ab%8b%e5%92%8c%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3%e5%90%91%e9%87%8f-%e7%8b%ac%e7%ab%8b-%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3\/"},"modified":"2023-09-16T13:05:25","modified_gmt":"2023-09-16T13:05:25","slug":"%e7%8b%ac%e7%ab%8b%e5%92%8c%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3%e5%90%91%e9%87%8f-%e7%8b%ac%e7%ab%8b-%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e7%8b%ac%e7%ab%8b%e5%92%8c%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3%e5%90%91%e9%87%8f-%e7%8b%ac%e7%ab%8b-%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3\/","title":{"rendered":"\u7ebf\u6027\u72ec\u7acb\u548c\u76f8\u5173\u5411\u91cf\uff08\u7ebf\u6027\u72ec\u7acb\u548c\u76f8\u5173\uff09"},"content":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u548c\u7ebf\u6027\u76f8\u5173\u5411\u91cf\u3002\u60a8\u8fd8\u5c06\u770b\u5230\u5982\u4f55\u5224\u65ad\u4e00\u7ec4\u5411\u91cf\u662f\u7ebf\u6027\u76f8\u5173\u8fd8\u662f\u72ec\u7acb\u7684\u793a\u4f8b\u3002\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u6709\u5173\u7ebf\u6027\u72ec\u7acb\u6027\u548c\u4f9d\u8d56\u6027\u7684\u7ec3\u4e60\u5e76\u9010\u6b65\u89e3\u51b3\u95ee\u9898\u3002 <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-vectores-linealmente-independientes\"><\/span>\u4ec0\u4e48\u662f\u7ebf\u6027\u65e0\u5173\u5411\u91cf\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u5982\u679c\u4e00\u7ec4\u81ea\u7531\u5411\u91cf\u4e2d\u6ca1\u6709\u4e00\u4e2a\u53ef\u4ee5\u5199\u6210\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u5b83\u4eec\u662f<strong>\u7ebf\u6027\u72ec\u7acb\u7684<\/strong>\u3002<\/p>\n<p style=\"text-align:left\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u7ec4\u5411\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-33729e6d20b00643b5d9ddf38544c11c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_1, \\vv{\\text{v}}_2,\\ldots \\vv{\\text{v}}_n,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5982\u679c\u4ee5\u4e0b\u65b9\u7a0b\u7684\u552f\u4e00\u89e3\u662f\u7ebf\u6027\u72ec\u7acb\u7684\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-300ebfc809f336b8eba997c6d2b17b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots + a_n\\vv{\\text{v}}_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"224\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u8fd9\u4e9b\u90fd\u662f\u6240\u6709\u7684\u7cfb\u6570<\/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-f91083f3035e5168a6f0b3e6335d6858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u7b49\u4e8e0\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-343093bdf0637093707400807a880327_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=\\dots = a_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"177\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p>\u51e0\u4f55\u4e0a\uff0c\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u4e0d\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\uff0c\u5373\u4e0d\u5e73\u884c\uff0c\u5219\u5b83\u4eec\u662f\u7ebf\u6027\u65e0\u5173\u7684\u3002<\/p>\n<p>\u4e3a\u4e86\u7b80\u6d01\u8d77\u89c1\uff0c\u6211\u4eec\u6709\u65f6\u76f4\u63a5\u8bf4\u5b83\u4eec\u662f LI \u5411\u91cf\u3002\u6216\u8005\u5411\u91cf\u5177\u6709\u7ebf\u6027\u72ec\u7acb\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-vectores-linealmente-dependientes\"><\/span>\u4ec0\u4e48\u662f\u7ebf\u6027\u76f8\u5173\u5411\u91cf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u663e\u7136\uff0c\u7ebf\u6027\u76f8\u5173\u5411\u91cf\u7684\u542b\u4e49\u4e0e\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u76f8\u53cd\u3002\u56e0\u6b64\u5b83\u7684\u5b9a\u4e49\u662f\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\">\u5982\u679c\u5e73\u9762\u7684\u4e00\u7ec4\u81ea\u7531\u5411\u91cf\u4e2d\u7684\u4efb\u4f55\u4e00\u4e2a\u53ef\u4ee5\u8868\u793a\u4e3a\u5f62\u6210\u7cfb\u7edf\u7684\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u5b83\u4eec\u662f<strong>\u7ebf\u6027\u76f8\u5173\u7684<\/strong>\u3002<\/p>\n<p style=\"text-align:left\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u7ed9\u5b9a\u4e00\u7ec4\u5411\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-33729e6d20b00643b5d9ddf38544c11c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_1, \\vv{\\text{v}}_2,\\ldots \\vv{\\text{v}}_n,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5982\u679c\u5b58\u5728\u4ee5\u4e0b\u65b9\u7a0b\u7684\u89e3\uff0c\u5219\u8fd9\u4e9b\u662f\u7ebf\u6027\u76f8\u5173\u7684\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-300ebfc809f336b8eba997c6d2b17b0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{v}}_1+a_2\\vv{\\text{v}}_2+\\dots + a_n\\vv{\\text{v}}_n=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"224\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\">\u5176\u4e2d\u6709\u4e00\u5b9a\u7684\u7cfb\u6570<\/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-f91083f3035e5168a6f0b3e6335d6858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u4e0e 0 \u4e0d\u540c\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-439f0ac04db138f5e47e7ffa3010ac82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_i\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"48\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p>\u53cd\u4e4b\u4ea6\u7136\uff1a\u5982\u679c\u4e00\u4e2a\u5411\u91cf\u662f\u5176\u4ed6\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u5219\u8be5\u96c6\u5408\u4e2d\u7684\u6240\u6709\u5411\u91cf\u90fd\u662f\u7ebf\u6027\u76f8\u5173\u7684\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u5e73\u884c\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u662f\u7ebf\u6027\u76f8\u5173\u7684\u3002<\/p>\n<p>\u6709\u65f6\u5b83\u4eec\u4e5f\u88ab\u7f29\u5199\u5e76\u7b80\u79f0\u4e3a LD \u5411\u91cf\u3002\u6216\u8005\u751a\u81f3\u5411\u91cf\u5177\u6709\u7ebf\u6027\u76f8\u5173\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-saber-si-los-vectores-son-linealmente-dependientes-o-independientes\"><\/span>\u5982\u4f55\u77e5\u9053\u5411\u91cf\u662f\u5426\u7ebf\u6027\u76f8\u5173\u6216\u72ec\u7acb\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u7ebf\u6027\u76f8\u5173\u5411\u91cf\u548c\u72ec\u7acb\u5411\u91cf\u7684\u5178\u578b\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u786e\u5b9a\u4ee5\u4e0b 3 \u4e2a 3 \u7ef4\u5411\u91cf\u662f\u5426\u5177\u6709\u7ebf\u6027\u76f8\u5173\u6027\u6216\u72ec\u7acb\u6027\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-05af06eeddc930d2a2a1aef3557f1804_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,5,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-8499337b8d833980eb798442df144157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" 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-cfab263ab4dab31ac33ce94bf5cd605a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (4,2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8bf4\u660e\u7ebf\u6027\u7ec4\u5408\u6761\u4ef6\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-2580c2225e7e01a88d80c323da49b776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}} + a_3\\vv{\\text{w}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u7528\u6bcf\u4e2a\u5411\u91cf\u7684\u5750\u6807\u66ff\u6362\u5b83\u3002\u548c\u96f6\u4e00\u6837\uff0c\u5bf9\u5e94\u96f6\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-7b93accc41aaa4124dbe17d48b613380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,5,2)+a_2(-2,3,-1)+ a_3(4,2,1)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u7cfb\u6570\u4e58\u4ee5\u5411\u91cf\uff0c\u56e0\u6b64\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u662f\u7b49\u6548\u7684\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-e862c54b435070e58979525edbd3982b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,5a_1,2a_1)+(-2a_2,3a_2,-a_2) + (4a_3,2a_3,a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"444\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u6dfb\u52a0\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-aeeebd2fc4c71c53bb5b69a7ba4712fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1-2a_2+4a_3 \\ , \\ 5a_1+3a_2+2a_3 \\ , \\ 2a_1-a_2+a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"468\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5982\u679c\u6211\u4eec\u4ed4\u7ec6\u89c2\u5bdf\uff0c\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u5bf9\u5e94\u4e8e 3 \u4e2a\u65b9\u7a0b\uff0c\u56e0\u4e3a\u5de6\u5411\u91cf\u7684\u6bcf\u4e2a\u5750\u6807\u5fc5\u987b\u7b49\u4e8e\u53f3\u5411\u91cf\u7684\u6bcf\u4e2a\u5750\u6807\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u7531 3 \u4e2a\u65b9\u7a0b\u548c 3 \u4e2a\u672a\u77e5\u6570\u7ec4\u6210\u7684\u9f50\u6b21\u65b9\u7a0b\u7ec4\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-c6bb8117dd8ae715314efe73fe65eed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1-2a_2+4a_3 = 0 \\\\[2ex] 5a_1+3a_2+2a_3 =0\\\\[2ex] 2a_1-a_2+a_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u552f\u4e00\u9700\u8981\u505a\u7684\u5c31\u662f\u6c42\u89e3\u672a\u77e5\u6570\u4e3a\u7684\u65b9\u7a0b\u7ec4<\/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-41a350e61a3992febcf5f69fdb79f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1, a_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: -4px;\"><\/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-5eff362725f9c8095e12f173e039328e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3.\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"21\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u4e3a\u6b64\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u4efb\u4f55\u65b9\u6cd5\uff08\u66ff\u6362\u6cd5\u3001\u9ad8\u65af\u6cd5\u3001\u514b\u83b1\u9ed8\u6cd5\u5219\u7b49\uff09\u3002\u7136\u800c\uff0c\u8981\u77e5\u9053\u5411\u91cf\u662f LI \u8fd8\u662f LD\uff0c\u53ea\u9700\u786e\u5b9a\u662f\u5426\u5b58\u5728\u9664\u5e73\u51e1\u89e3\uff08\u6240\u6709\u7cfb\u6570\u90fd\u4e3a\u96f6\uff09\u4e4b\u5916\u7684\u89e3\u5c31\u8db3\u591f\u4e86\u3002\u6240\u4ee5\uff1a <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 12px; border: 2px solid #FFB74D; border-radius:20px;\">\n<ul>\n<li style=\"margin-bottom:24px\">\u5982\u679c\u7531\u5411\u91cf\u5206\u91cf\u7ec4\u6210\u7684\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff0c\u5219\u610f\u5473\u7740\u65b9\u7a0b\u7ec4\u53ea\u6709\u4e00\u4e2a\u89e3\uff08\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-485cb2ce7f28253bda0a1262eeec81b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=a_3=\\dots=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"175\" style=\"vertical-align: -3px;\"><\/p>\n<p> \uff09\uff0c\u56e0\u6b64\u5411\u91cf\u662f<strong>\u7ebf\u6027\u65e0\u5173\u7684<\/strong><\/li>\n<li style=\"margin-bottom:14px\">\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u7531\u5411\u91cf\u5206\u91cf\u7ec4\u6210\u7684\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7b49\u4e8e\u96f6\uff0c\u5219\u610f\u5473\u7740\u65b9\u7a0b\u7ec4\u5177\u6709\u591a\u4e2a\u89e3\uff0c\u56e0\u6b64\u5411\u91cf\u662f<strong>\u7ebf\u6027\u76f8\u5173\u7684<\/strong>\u3002<\/li>\n<\/ul>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u552f\u4e00\u9700\u8981\u8ba1\u7b97\u7684\u662f\u5411\u91cf\u5750\u6807\u7684\u884c\u5217\u5f0f\uff08\u56e0\u4e3a\u5b83\u662f\u4e00\u4e2a 3&#215;3 \u884c\u5217\u5f0f\uff0c\u6240\u4ee5\u53ef\u4ee5\u7528 Sarrus \u89c4\u5219\u6c42\u89e3\uff09\u3002\u8be5\u884c\u5217\u5f0f\u5bf9\u5e94\u4e8e\u5148\u524d\u65b9\u7a0b\u7ec4\u7684\u7cfb\u6570\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-046e05ff603822985510c7bdc8b73021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;-2&amp;4\\\\[1.1ex] 5&amp;3&amp;2 \\\\[1.1ex] 2&amp;-1&amp;1 \\end{vmatrix} = -37 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u884c\u5217\u5f0f\u4e0d\u4e3a 0\uff0c\u56e0\u6b64\u5411\u91cf\u662f<strong>\u7ebf\u6027\u65e0\u5173\u7684<\/strong>\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u65b9\u7a0b\u7ec4\u552f\u4e00\u53ef\u80fd\u7684\u89e3\u662f\u6240\u6709\u672a\u77e5\u6570\u90fd\u4e3a\u96f6\u7684\u5e73\u51e1\u89e3\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-55102cbf302a51cdb904a4f3ad88e658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1=a_2=a_3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"131\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-los-vectores-linealmente-dependientes-e-independientes\"><\/span>\u7ebf\u6027\u76f8\u5173\u548c\u72ec\u7acb\u5411\u91cf\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p>\u5411\u91cf\u7684\u7ebf\u6027\u76f8\u5173\u6027\u6216\u72ec\u7acb\u6027\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\u4e24\u4e2a\u6bd4\u4f8b\u5411\u91cf\u662f\u5e73\u884c\u7684\uff0c\u56e0\u6b64\u7ebf\u6027\u76f8\u5173\uff0c\u56e0\u4e3a\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u540c\u6837\uff0c\u5982\u679c\u4e24\u4e2a\u5411\u91cf\u65b9\u5411\u4e0d\u540c\u6216\u4e0d\u6210\u6bd4\u4f8b\uff0c\u5219\u5b83\u4eec\u662f\u7ebf\u6027\u65e0\u5173\u7684\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4e09\u4e2a\u5171\u9762\u5411\u91cf\uff08\u4f4d\u4e8e\u540c\u4e00\u5e73\u9762\u5185\uff09\u7ebf\u6027\u65e0\u5173\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u96f6\u5411\u91cf\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8606fdc9522ef08a3d4b889a3d840_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}=(0,0,0))\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u7ebf\u6027\u4f9d\u8d56\u4e8e\u4efb\u4f55\u5411\u91cf\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4e00\u7ec4\u7ebf\u6027\u65e0\u5173\u7684\u5411\u91cf\u751f\u6210\u5411\u91cf\u7a7a\u95f4\u5e76\u5f62\u6210\u5411\u91cf\u57fa\u3002\u5982\u679c\u4e09\u4e2a\u5411\u91cf\u5782\u76f4\uff0c\u5219\u5b83\u662f\u6b63\u4ea4\u57fa\u3002\u5982\u679c\u5b83\u7684\u6a21\u4e5f\u7b49\u4e8e 1\uff0c\u5219\u8fd9\u5bf9\u5e94\u4e8e\u6807\u51c6\u6b63\u4ea4\u57fa\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-dependencia-e-independencia-lineal\"><\/span>\u89e3\u51b3\u4e86\u7ebf\u6027\u76f8\u5173\u6027\u548c\u72ec\u7acb\u6027\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0b\u9762\u6709\u51e0\u4e2a\u5173\u4e8e\u7ebf\u6027\u76f8\u5173\u548c\u72ec\u7acb\u5411\u91cf\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\u53ef\u4f9b\u7ec3\u4e60\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b\u5411\u91cf\u662f\u7ebf\u6027\u76f8\u5173\u8fd8\u662f\u72ec\u7acb\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-d552b4aa1666be818679ed4557aa7950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,-2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-044b61524cd81ac5ea271deaf60ba56f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (2,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" 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-5f2e178b7cbb93d5b58a5a9d493b3e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (5,-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"><\/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__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" 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\u63d0\u51fa\u7ebf\u6027\u7ec4\u5408\u6761\u4ef6\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-2580c2225e7e01a88d80c323da49b776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}} + a_3\\vv{\\text{w}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -3px;\"><\/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-62dca064bc122d1180bd344cc63b09ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,-2,1)+a_2(2,1,3)+ a_3(5,-1,1)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" 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-358964cb9ab1a6719cd7fac6d80f35bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,-2a_1,a_1)+(2a_2,a_2,3a_2) + (5a_3,-a_3,a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"427\" 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-4a60f9dd00a04a5d988a9d664befa3fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1+2a_2+5a_3 \\ , \\ -2a_1+a_2-a_3 \\ , \\ a_1+3a_2+a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"464\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u524d\u9762\u7684\u7b49\u5f0f\u5bf9\u5e94\u4e8e\u4ee5\u4e0b\u7ebf\u6027\u65b9\u7a0b\u7ec4\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-58f1b449f48096570437df0ca40f8a8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1+2a_2+5a_3 = 0 \\\\[2ex] -2a_1+a_2-a_3 =0\\\\[2ex] a_1+3a_2+a_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"171\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u8868\u8ff0\u4e86\u65b9\u7a0b\u7ec4\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u7528\u5b83\u7684\u9879\u6765\u6c42\u89e3\u77e9\u9635\u7684\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-caa6d4f135e79bb8b6d2368ff7eebefb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;2&amp;5\\\\[1.1ex] -2&amp;1&amp;-1 \\\\[1.1ex] 1&amp;3&amp;1 \\end{vmatrix} = -29 \\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"179\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u884c\u5217\u5f0f\u4e0d\u4e3a0\uff0c\u56e0\u6b64\u4e09\u4e2a\u5411\u91cf\u5f7c\u6b64<strong>\u7ebf\u6027\u65e0\u5173<\/strong>\u3002<\/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>\u5c06\u4ee5\u4e0b\u5411\u91cf\u5206\u7c7b\u4e3a\u7ebf\u6027\u76f8\u5173\u6216\u72ec\u7acb\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-4cc2ed855100fa8f5ef4d5a58eec547c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-1511660305e564364f81511fbcab382a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,0,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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-82f0ad7c365ea32003750cc4b55e44f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (3,-1,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -5px;\"><\/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__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" 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\u6211\u4eec\u63d0\u51fa\u7ebf\u6027\u7ec4\u5408\u7684\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-2580c2225e7e01a88d80c323da49b776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}} + a_3\\vv{\\text{w}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -3px;\"><\/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-28ebfd8d5f95694329a88caf6213a263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(1,4,3)+a_2(-2,0,2)+ a_3(3,-1,-4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" 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-9e75b345f90c95164ef95890f9fd67ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1,4a_1,3a_1)+(-2a_2,0,2a_2) + (3a_3,-a_3,-4a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"450\" 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-221296d40e44e447a90dcdbb00752663_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a_1-2a_2+3a_3 \\ , \\ 4a_1-a_3 \\ , \\ 3a_1+2a_2-4a_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"429\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6839\u636e\u524d\u9762\u7684\u7b49\u5f0f\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u9f50\u6b21\u65b9\u7a0b\u7ec4\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-c94610b6f8baef34a1fb4601c148f515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} a_1-2a_2+3a_3= 0 \\\\[2ex] 4a_1-a_3 =0\\\\[2ex] 3a_1+2a_2-4a_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u8868\u8ff0\u4e86\u65b9\u7a0b\u7ec4\uff0c\u6211\u4eec\u5c31\u7528\u5411\u91cf\u7684\u5750\u6807\u6c42\u89e3\u77e9\u9635\u7684\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-67678c37fdaf0955ef8bbab8d34379f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 1&amp;-2&amp;3\\\\[1.1ex] 4&amp;0&amp;-1 \\\\[1.1ex] 3&amp;2&amp;-4 \\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u884c\u5217\u5f0f\u76f8\u5f53\u4e8e 0\uff0c\u56e0\u6b64\u4e09\u4e2a\u5411\u91cf\u5f7c\u6b64<strong>\u7ebf\u6027\u76f8\u5173<\/strong>\u3002<\/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>\u5bf9\u4e8e\u4ee5\u4e0b\u4e09\u4e2a\u5411\u91cf\uff0c\u6307\u51fa\u54ea\u4e9b\u5411\u91cf\u5bf9\u662f\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u54ea\u4e9b\u5bf9\u662f\u7ebf\u6027\u65e0\u5173\u7684\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-c53b2414f85df7b5510ea6f379ad9c59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (1,2,-2) \\qquad \\vv{\\text{v}} = (2,4,-3) \\qquad \\vv{\\text{w}} = (-4,-8,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"397\" style=\"vertical-align: -5px;\"><\/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__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" 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\">\u5224\u65ad\u4e00\u5bf9\u5411\u91cf\u662f\u5426\u7ebf\u6027\u76f8\u5173\u6216\u72ec\u7acb\u7684\u6700\u7b80\u5355\u65b9\u6cd5\u662f\u68c0\u67e5\u5b83\u4eec\u662f\u5426\u6210\u6bd4\u4f8b\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u9996\u5148\u68c0\u67e5\u5411\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-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e\u5411\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f5713006a9840d2d71efbe7b540d21a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-2e9f2e572ec99322a57982b9cb393ca8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{2}{4} \\neq \\cfrac{-2}{-3} \\ \\longrightarrow \\ \\text{LI}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"167\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u6b21\uff0c\u6211\u4eec\u68c0\u67e5\u5411\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-cac24ae79c1e4cbc459f01ed5e4f824e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e\u5411\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cea7925862c08ac4cf5b4963c0187b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-034dc83f2bfec42f9cf743d295f52feb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{-4} = \\cfrac{2}{-8} \\neq \\cfrac{-2}{6} \\ \\longrightarrow \\ \\text{LI}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"194\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u6d4b\u8bd5\u5411\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-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4e0e\u5411\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97cea7925862c08ac4cf5b4963c0187b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} :\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-bf4a92d82a160dae8ee8ca41cfad22ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{-4} = \\cfrac{4}{-8} = \\cfrac{-3}{6} = -\\cfrac{1}{2} \\ \\longrightarrow \\ \\text{Proporcionales}\\ \\longrightarrow \\ \\text{LD}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"414\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u552f\u4e00\u4e00\u5bf9\u5f7c\u6b64\u7ebf\u6027\u4f9d\u8d56\u7684\u5411\u91cf\u662f<\/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-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" 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-d8af8ced46d93e73dc5290e0cca4dc6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u6b64\u5916\uff0c\u5b83\u4eec\u7684\u5173\u7cfb\u5982\u4e0b\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-b3184c3260a84d9f7722440a1b95392f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= -\\cfrac{1}{2} \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"71\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6216\u540c\u7b49\u5b66\u5386\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-5a599602f8553abe4f0fb99e3efd3966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}}= -2\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"68\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u5176\u4ed6\u5411\u91cf\u5bf9\u662f\u7ebf\u6027\u65e0\u5173\u7684\u3002<\/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>\u7814\u7a76\u4ee5\u4e0b 4 \u4e2a\u5411\u91cf\u5f7c\u6b64\u4e4b\u95f4\u7684\u7ebf\u6027\u76f8\u5173\u6027\u6216\u72ec\u7acb\u6027\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-32b4b70627510756dee79c34319889d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (0,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" 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-fa38827f1af905436c7ac1b64da780d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-1,-2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" 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-3b827cfdbb2751b83b0dfa8e571f20cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (4,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" 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-25ba65cf2ebddf211e70958fed7a6dd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{x}} = (-2,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/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__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" 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\u63d0\u51fa\u7ebf\u6027\u7ec4\u5408\u6761\u4ef6\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-75cb11870b19756a745d82caf5ecba82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}} + a_3\\vv{\\text{w}}+a_4\\vv{\\text{x}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"207\" style=\"vertical-align: -3px;\"><\/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-6bd2e86f772066a8ad2255f8dffa054d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(0,1,2)+a_2(-1,-2,0)+ a_3(4,1,-1)+a_4(-2,-3,2)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"506\" 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-192de9f156d81073e6e0b3815fe6703a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(0,a_1,2a_1)+(-a_2,-2a_2,0) +(4a_3,a_3,-a_3)+(-2a_4,-3a_4,2a_4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"572\" 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-828034966309aab74913c929b3781e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-a_2+4a_3-2a_4\\ , \\ a_1-2a_2+a_3-3a_4 \\ , \\ 2a_1-a_3+2a_4)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"520\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728\u672c\u4f8b\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u5305\u542b 3 \u4e2a\u65b9\u7a0b\u7ec4\u548c 4 \u4e2a\u672a\u77e5\u6570\u7684\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-e9451263e5a31994569292e32666d93e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} -a_2+4a_3-2a_4 = 0 \\\\[2ex] a_1-2a_2+a_3-3a_4 =0\\\\[2ex] 2a_1-a_3+2a_4 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u65e0\u6cd5\u6c42\u89e3\u6574\u4e2a\u7cfb\u7edf\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff0c\u56e0\u4e3a\u53ea\u80fd\u786e\u5b9a\u65b9\u9635\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u8ba1\u7b97 3\u00d73 \u884c\u5217\u5f0f\u7684\u6240\u6709\u53ef\u80fd\u7ec4\u5408\uff0c\u5e76\u67e5\u770b\u5176\u4e2d\u4e00\u4e2a\u662f\u5426\u7b49\u4e8e 0\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5411\u91cf\u5c06\u7ebf\u6027\u76f8\u5173\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6240\u6709\u884c\u5217\u5f0f\u90fd\u4e0d\u540c\u4e8e 0\uff0c\u5219 4 \u4e2a\u5411\u91cf\u5c06\u662f\u7ebf\u6027\u72ec\u7acb\u7684\u3002<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u8ba1\u7b97\u7cfb\u6570\u7684\u884c\u5217\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-41a350e61a3992febcf5f69fdb79f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1, a_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: -4px;\"><\/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-a5e5ed86162a9b0324b8f44dc16fcbce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_3:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/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-488d7848a40aa9a91bd5b3aa1f09b774_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 0&amp;-1&amp;4\\\\[1.1ex] 1&amp;-2&amp;1 \\\\[1.1ex] 2&amp;0&amp;-1 \\end{vmatrix} =13\\bm{\\neq 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u524d 3 \u4e2a\u7cfb\u6570\uff08\u6216\u524d 3 \u4e2a\u5411\u91cf\uff09\u7684\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\u3002\u73b0\u5728\u6211\u4eec\u5c1d\u8bd5\u4f7f\u7528\u7cfb\u6570\u7684\u884c\u5217\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-41a350e61a3992febcf5f69fdb79f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1, a_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: -4px;\"><\/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-f76864c5409cf2dea96ed29cc6bf43c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_4:\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"26\" style=\"vertical-align: -3px;\"><\/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-d1475a77f10ea0c16147a6f9c3f611b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 0&amp;-1&amp;-2\\\\[1.1ex] 1&amp;-2&amp;-3 \\\\[1.1ex] 2&amp;0&amp;2 \\end{vmatrix} \\bm{= 0}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u83b7\u5f97\u4e86\u96f6\u884c\u5217\u5f0f\uff0c\u56e0\u6b64\u65e0\u9700\u8ba1\u7b97\u5176\u4ed6\u884c\u5217\u5f0f\uff0c\u56e0\u4e3a\u6211\u4eec\u5df2\u7ecf\u77e5\u9053 4 \u4e2a\u5411\u91cf\u662f<strong>\u7ebf\u6027\u76f8\u5173\u7684<\/strong>\u3002<\/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>\u8ba1\u7b97\u503c<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u4f7f\u5f97\u4ee5\u4e0b\u5411\u91cf\u662f\u7ebf\u6027\u65e0\u5173\u7684\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-edc48924ce57971f9c5940e09d028aff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} = (3,-1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" 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-88c00cd3b8e4f88f1092a5fb484cd5fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}} = (-2,4,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" 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-d2848445bf3f500e9635da849a0fa1d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{w}} = (1,3,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\"><\/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__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" 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\u6211\u4eec\u63d0\u51fa\u7ebf\u6027\u7ec4\u5408\u7684\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-2580c2225e7e01a88d80c323da49b776_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1\\vv{\\text{u}}+a_2\\vv{\\text{v}} + a_3\\vv{\\text{w}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"159\" style=\"vertical-align: -3px;\"><\/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-b94523fdc15d85da997726f01a1df5b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_1(3,-1,5)+a_2(-2,4,7)+ a_3(1,3,k)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" 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-78e6c627ddd8e0bd7070c329152ba135_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3a_1,-a_1,5a_1)+(-2a_2,4a_2,7a_2) + (a_3,3a_3,ka_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"454\" 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-cccd303f53e73d03d6f47d3694d09b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3a_1-2a_2+a_3 \\ , \\ -a_1+4a_2+3a_3 \\ , \\ 5a_1+7a_2+ka_3)=(0,0,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"492\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4ece\u524d\u9762\u7684\u5411\u91cf\u65b9\u7a0b\uff0c\u6211\u4eec\u5f97\u5230\u4ee5\u4e0b\u9f50\u6b21\u65b9\u7a0b\u7ec4\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-16f88cbf406c1faf61307b99179a5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l}3a_1-2a_2+a_3= 0 \\\\[2ex] -a_1+4a_2+3a_3 =0\\\\[2ex] 5a_1+7a_2+ka_3 = 0 \\end{array} \\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"97\" width=\"180\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e00\u65e6\u6211\u4eec\u8868\u8ff0\u4e86\u65b9\u7a0b\u7ec4\uff0c\u6211\u4eec\u5c31\u5c1d\u8bd5\u6c42\u89e3\u8be5\u65b9\u7a0b\u7ec4\u7684\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-d748080bb1cacc1c80a35ef633a2d85e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 3&amp;-2&amp;1\\\\[1.1ex] -1&amp;4&amp;3 \\\\[1.1ex] 5&amp;7&amp;k \\end{vmatrix} =10k-120\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"197\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u9648\u8ff0\u544a\u8bc9\u6211\u4eec\u5411\u91cf\u5fc5\u987b\u662f\u7ebf\u6027\u76f8\u5173\u7684\u3002\u56e0\u6b64\u884c\u5217\u5f0f\u5fc5\u987b\u7b49\u4e8e\u96f6\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-a0d1aeff1b4ba348b51bb226997d7202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 10k-120=0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"107\" 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-b98ff23cda28486515d12ef26c8a0e25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 10k=120\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"77\" 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-4177c59fe629665dcf7a57de632b85ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle k=\\cfrac{120}{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"62\" style=\"vertical-align: -12px;\"><\/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-32770a08083461fbb6a7260627d6a9c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{k=12}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8be5\u5e38\u6570\u5fc5\u987b\u7b49\u4e8e 12\uff0c\u4ee5\u4fbf\u77e2\u91cf\u5177\u6709\u7ebf\u6027\u76f8\u5173\u6027\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u672c\u9875\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u548c\u7ebf\u6027\u76f8\u5173\u5411\u91cf\u3002\u60a8\u8fd8\u5c06\u770b\u5230\u5982\u4f55\u5224\u65ad\u4e00\u7ec4\u5411\u91cf\u662f\u7ebf\u6027\u76f8\u5173\u8fd8\u662f\u72ec\u7acb\u7684\u793a\u4f8b\u3002\u6b64\u5916\uff0c &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e7%8b%ac%e7%ab%8b%e5%92%8c%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3%e5%90%91%e9%87%8f-%e7%8b%ac%e7%ab%8b-%e7%ba%bf%e6%80%a7%e7%9b%b8%e5%85%b3\/\"> <span class=\"screen-reader-text\">\u7ebf\u6027\u72ec\u7acb\u548c\u76f8\u5173\u5411\u91cf\uff08\u7ebf\u6027\u72ec\u7acb\u548c\u76f8\u5173\uff09<\/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":[21],"tags":[],"class_list":["post-69","post","type-post","status-publish","format-standard","hentry","category-21"],"yoast_head":"<!-- This site is optimized 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