{"id":259,"date":"2023-07-10T06:51:49","date_gmt":"2023-07-10T06:51:49","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e7%82%b9%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/"},"modified":"2023-07-10T06:51:49","modified_gmt":"2023-07-10T06:51:49","slug":"%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e7%82%b9%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e7%82%b9%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/","title":{"rendered":"\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9\u4ee5\u53ca\u5982\u4f55\u77e5\u9053\u67d0\u4e9b\u70b9\u662f\u5426\u5171\u9762\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u5171\u9762\u70b9\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-puntos-coplanarios\"><\/span>\u4ec0\u4e48\u662f\u5171\u9762\u70b9\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u89e3\u6790\u51e0\u4f55\u4e2d\uff0c\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9\u7684\u542b\u4e49\u5982\u4e0b\uff1a<\/p>\n<p><strong>\u5171\u9762\u70b9\u662f\u5c5e\u4e8e\u540c\u4e00\u5e73\u9762\u7684\u70b9\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c2 \u6216 3 \u4e2a\u70b9\u603b\u662f\u5171\u9762\uff0c\u56e0\u4e3a\u53ea\u9700 3 \u4e2a\u70b9\u5373\u53ef\u5f62\u6210\u4e00\u4e2a\u5e73\u9762\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u6709 4 \u4e2a\u30015 \u4e2a\u6216\u66f4\u591a\u4e2a\u70b9\u65f6\uff0c\u67d0\u4e9b\u70b9\u53ef\u80fd\u4e0d\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\uff0c\u56e0\u6b64\u5b83\u4eec\u4e0d\u5171\u9762\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/points-coplanaires.webp\" alt=\"\u5171\u9762\u70b9\" class=\"wp-image-3165\" width=\"411\" height=\"215\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4f8b\u5982\uff0c\u5728\u4e0a\u9762\u7684\u56fe\u5f62\u8868\u793a\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u70b9 A\u3001C\u3001D \u548c F \u5f7c\u6b64\u5171\u9762\uff0c\u56e0\u4e3a\u5b83\u4eec\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u4e2d\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u8fd94\u4e2a\u70b9\u4e0eB\u3001E\u3001G\u70b9\u4e0d\u5171\u9762\uff0c\u56e0\u4e3a\u5728\u5305\u542b\u6240\u6709\u70b9\u7684\u7a7a\u95f4\u4e2d\u65e0\u6cd5\u5f62\u6210\u5e73\u9762\u3002<\/p>\n<p>\u4ece\u8fd9\u4e2a\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u5171\u9762\u70b9\u5b9a\u4e49\u7684\u5411\u91cf\u4e5f\u662f\u5171\u9762\u5411\u91cf\uff0c\u5373\u5b83\u4eec\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u5185\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuando-los-puntos-son-coplanarios\"><\/span>\u70b9\u4ec0\u4e48\u65f6\u5019\u5171\u9762\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9\u7684\u5b9a\u4e49\u4e2d\u770b\u5230\u7684\uff0c\u4e24\u4e2a\u6216\u4e09\u4e2a\u70b9\u603b\u662f\u5171\u9762\u7684\uff0c\u4f46\u8d85\u8fc7\u4e09\u4e2a\u70b9\u5219\u4e0d\u5fc5\u9075\u5b88\u5171\u9762\u5173\u7cfb\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5224\u65ad\u56db\u4e2a\u6216\u66f4\u591a\u70b9\u662f\u5426\u5171\u9762\u4e3b\u8981\u6709\u4e24\u79cd\u65b9\u6cd5\uff1a<\/p>\n<ul>\n<li>\u4e86\u89e3\u70b9\u662f\u5426\u5171\u9762\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u901a\u8fc7\u70b9\u786e\u5b9a\u7684\u5411\u91cf\uff1a<strong>\u5982\u679c\u8fd9\u4e9b\u5411\u91cf\u5171\u9762<\/strong>\uff0c\u5219\u8fd9\u4e9b\u70b9\u4e5f\u5171\u9762\u3002<\/li>\n<\/ul>\n<p>\u663e\u7136\uff0c\u8981\u5e94\u7528\u6b64\u65b9\u6cd5\uff0c\u60a8\u9700\u8981\u77e5\u9053\u5411\u91cf\u4f55\u65f6\u5171\u9762\u3002\u4f46\u7531\u4e8e\u8fd8\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u786e\u5b9a\u4e00\u7ec4\u5411\u91cf\u662f\u5426\u5171\u9762\uff0c\u56e0\u6b64\u6211\u4eec\u5efa\u8bae\u68c0\u67e5<a href=\"https:\/\/mathority.org\/cn\/\u5171\u9762\u6216\u5171\u9762\u5411\u91cf\/\">\u5982\u4f55\u5224\u65ad\u5411\u91cf\u662f\u5426\u5171\u9762<\/a>\u3002\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u67e5\u627e 2\u30013\u30014 \u6216\u66f4\u591a\u5411\u91cf\u4f55\u65f6\u5171\u9762\u7684\u6240\u6709\u73b0\u6709\u7a0b\u5e8f\uff0c\u4ee5\u53ca\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002<\/p>\n<ul>\n<li>\u77e5\u9053\u4e00\u7ec4\u70b9\u662f\u5426\u5171\u9762\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f<strong><a href=\"https:\/\/mathority.org\/cn\/\u7a7a\u95f4\u5e73\u9762\u65b9\u7a0b\/\">\u627e\u5230\u8be5\u7ec4\u4e2d3\u4e2a\u70b9\u6240\u5f62\u6210\u7684\u5e73\u9762\u7684\u65b9\u7a0b<\/a><\/strong>\uff0c\u5982\u679c\u5176\u4ed6\u70b9\u6ee1\u8db3\u8be5\u65b9\u7a0b\uff0c\u5219\u8fd9\u610f\u5473\u7740\u8be5\u7ec4\u4e2d\u7684\u6240\u6709\u70b9\u90fd\u662f\u5171\u9762\u7684\u3002<\/li>\n<\/ul>\n<p>\u5c3d\u7ba1\u8fd9\u53d6\u51b3\u4e8e\u95ee\u9898\uff0c\u4f46\u6211\u4eec\u5efa\u8bae\u4f7f\u7528\u8fd9\u4e24\u79cd\u65b9\u6cd5\u4e2d\u7684\u7b2c\u4e00\u79cd\uff0c\u56e0\u4e3a\u68c0\u67e5\u5411\u91cf\u662f\u5426\u5171\u9762\u6bd4\u8ba1\u7b97\u5e73\u9762\u65b9\u7a0b\u8981\u7b80\u5355\u5feb\u6377\u5f97\u591a\u3002\u4f46\u662f\uff0c\u663e\u7136\uff0c\u4f7f\u7528\u60a8\u559c\u6b22\u7684\u4efb\u4f55\u4e00\u4e2a\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-puntos-coplanarios\"><\/span>\u89e3\u51b3\u4e86\u5171\u9762\u70b9\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u5224\u65ad\u4ee5\u4e0b\u4e09\u70b9\u662f\u5426\u5171\u9762\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-9a6d39406adb983eaad3c40c2e5d352c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,5,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-a2db4553e8942cf714a98783699f44f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(0,-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" 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-93a412e1bb305cd785882fd481852c9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(4,-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u65e0\u9700\u8fdb\u884c\u4efb\u4f55\u8ba1\u7b97\uff0c\u56e0\u4e3a<strong>3 \u4e2a\u70b9\u59cb\u7ec8\u5171\u9762<\/strong>\uff0c\u65e0\u8bba\u5b83\u4eec\u662f\u4ec0\u4e48\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>\u5224\u65ad\u4ee5\u4e0b\u56db\u70b9\u662f\u5426\u5171\u9762\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-adbc97b4e3f0c30a1cd47fb6eea0b566_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-d5ca7779c360bcb8ad9cf4d6b6a455a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(-1,3,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" 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-8910b93724e6f59b070ee26673c9426a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(1,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-6d40d5bb66afe9a8e8445cdb8b7cac0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(2,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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\">\u4e3a\u4e86\u4f7f\u56db\u4e2a\u70b9\u5171\u9762\uff0c\u7531\u5b83\u4eec\u786e\u5b9a\u7684\u5411\u91cf\u5fc5\u987b\u5171\u9762\u3002\u56e0\u6b64\u6211\u4eec\u8ba1\u7b97\u8fd9\u4e9b\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-e7922b55a4e968ce9ef945ddf4b0973e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (-1,3,4)-(1,2,0) = (-2,1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-8dfa4c2463f3a69890706b0387f1fbc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C- A = (1,0,-1)-(1,2,0) = (0,-2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"378\" 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-e5617a7317e2c18fcb39b3be782e26c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD} = D- A = (2,5,-3)-(1,2,0) = (1,3,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"367\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u6784\u9020\u7531\u5411\u91cf\u5f62\u6210\u7684\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-873ec750665fdf215a648778d6fcf042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} -2&amp;1&amp;4 \\\\[1.1ex]0&amp;-2&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-3\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"164\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u7ed3\u679c\u5411\u91cf\u5171\u9762\uff0c\u524d\u4e00\u4e2a\u77e9\u9635\u7684\u79e9\u5fc5\u987b\u7b49\u4e8e 2\u3002\u4e3a\u6b64\uff0c\u6574\u4e2a 3\u00d73 \u77e9\u9635\u7684\u884c\u5217\u5f0f\u5fc5\u987b\u7b49\u4e8e 0\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-18eb85dd3870c1e7c865705200cf6414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-3eadb62f19c07b8a646fe9b2a00f9003_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -2&amp;1&amp;4 \\\\[1.1ex]0&amp;-2&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-3\\end{vmatrix} =-11\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"198\" 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-466d66279a42e8aeb422d568e1547ef9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)=3\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u800c\uff0c\u6574\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e0d\u4e3a\u96f6\uff0c\u56e0\u6b64\u77e9\u9635\u7684\u79e9\u4e3a3\uff0c\u56e0\u6b64<strong>4\u4e2a\u70b9\u4e0d\u5171\u9762<\/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>\u5224\u65ad\u4ee5\u4e0b\u4e94\u70b9\u662f\u5426\u5171\u9762\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-083776221bb4167cd960c67da2435d9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-1a43aebd7e3c897898050e7440b0fe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(0,0,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" 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-59e69260b8e3baacdfd4f673aeb87fba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(4,-2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" 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-e862d9c0d7c715b2268b594c199f506a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(-1,1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" 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-f361ff1c29cf0a1dba88da8bdb1fb448_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E(2,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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\">\u4e3a\u4e86\u4f7f\u6240\u6709\u4e94\u4e2a\u70b9\u5171\u9762\uff0c\u5b83\u4eec\u5b9a\u4e49\u7684\u5411\u91cf\u4e5f\u5fc5\u987b\u5171\u9762\u3002\u56e0\u6b64\u6211\u4eec\u8ba1\u7b97\u8fd9\u4e9b\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-9b6a321df8b7b3e37dc31bf0cb9542dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (0,0,2)-(3,1,1) = (-3,-1,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-611bc1c76bcadfe27e2a793128a5a3c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C- A = (4,-2,-1)-(3,1,1) = (1,-3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"392\" 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-0ff805267450b865998e62bbc20111b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD} = D- A = (-1,1,3)-(3,1,1) = (-4,0,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"366\" 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-494b794700c9c99091abf0fd59523dd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AE} = E- A = (2,4,3)-(3,1,1) = (-1,3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u73b0\u5728\u8ba9\u6211\u4eec\u6784\u9020\u7531\u5411\u91cf\u7ec4\u6210\u7684\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d571ea172dbf5e6b7d85da6db466eb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} -3&amp;-1&amp;1 \\\\[1.1ex]1&amp;-3&amp;-2 \\\\[1.1ex] -4&amp;0&amp;2\\\\[1.1ex] -1&amp;3&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"164\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u751f\u6210\u7684\u5411\u91cf\u5171\u9762\uff0c\u524d\u4e00\u4e2a\u77e9\u9635\u7684\u79e9\u5fc5\u987b\u7b49\u4e8e 2\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u8fc7\u884c\u5217\u5f0f\u8ba1\u7b97\u5411\u91cf\u77e9\u9635\u7684\u79e9\uff0c\u4ee5\u68c0\u67e5\u5b83\u4eec\u662f\u5426\u5171\u9762\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-18eb85dd3870c1e7c865705200cf6414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)= \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-bec15883d9e3aa5a401afa41cd3992ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -3&amp;-1&amp;1 \\\\[1.1ex]1&amp;-3&amp;-2 \\\\[1.1ex] -4&amp;0&amp;2\\end{vmatrix} = 0 \\qquad \\begin{vmatrix} -3&amp;-1&amp;1 \\\\[1.1ex]1&amp;-3&amp;-2 \\\\[1.1ex] -1&amp;3&amp;2\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"326\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cd2f8cfa577e91b74c69e50cc36dfd9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -3&amp;-1&amp;1 \\\\[1.1ex] -4&amp;0&amp;2\\\\[1.1ex] -1&amp;3&amp;2\\end{vmatrix} = 0 \\qquad \\begin{vmatrix} 1&amp;-3&amp;-2 \\\\[1.1ex] -4&amp;0&amp;2\\\\[1.1ex] -1&amp;3&amp;2\\end{vmatrix} = 0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"312\" 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-d551dddceb916cc6cf8bf4137903da1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -3&amp;-1 \\\\[1.1ex] 1&amp;-3\\end{vmatrix} =10\\neq  0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" 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-6865ac4ae80c8b5a6eff791a9da5a937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A)=2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u77e9\u9635\u7684\u79e9\u76f8\u5f53\u4e8e2\uff0c\u56e0\u6b64\u5411\u91cf\u662f\u5171\u9762\u7684\uff0c\u56e0\u6b64<strong>5\u4e2a\u70b9\u4e5f\u662f\u5171\u9762\u7684\u3002<\/strong><\/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\u53c2\u6570\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 4 \u70b9\u5171\u9762\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-9483cca4fc2a94923b7c72ed89fc2d5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,1,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" 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-a5b113e265916c03a6de0547cfeb380b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(2,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"70\" 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-add9ad10fb8badd9de84f8ad1dcfe38d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(0,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" 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-8d5054a3ce659090916cda61b74f60bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(3,2,k)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" 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\">\u4e3a\u4e86\u4f7f\u56db\u4e2a\u70b9\u5171\u9762\uff0c\u7531\u5b83\u4eec\u786e\u5b9a\u7684\u5411\u91cf\u5fc5\u987b\u5171\u9762\u3002\u56e0\u6b64\u6211\u4eec\u8ba1\u7b97\u8fd9\u4e9b\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-996a90c58f67665e4a68e9dd4de6c718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (2,1,2)-(3,1,4) = (-1,0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-ae552981d5729c931f5bbb26c133ecc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C- A = (0,-1,3)-(3,1,4) = (-3,-2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"392\" 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-91aec8ed49541d8c2d8ca0b3b1f8a20d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD} = D- A = (3,2,k)-(3,1,4) = (0,1,k-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"371\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5176\u5411\u91cf\u77e9\u9635\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-c3d801efcf5b56dd858890720797d6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} -1&amp;0&amp;-2 \\\\[1.1ex] -3&amp;-2&amp;-1 \\\\[1.1ex] 0&amp;1&amp;k-4\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"181\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u4f7f\u6240\u5f97\u5411\u91cf\u5171\u9762\uff0c\u77e9\u9635\u7684\u79e9\u5fc5\u987b\u4e3a 2\u3002\u56e0\u6b64\uff0c\u6574\u4e2a 3&#215;3 \u77e9\u9635\u7684\u884c\u5217\u5f0f\u5fc5\u987b\u4e3a 0\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-bb7d3b31c10096d100843d781a85b621_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} -1&amp;0&amp;-2 \\\\[1.1ex] -3&amp;-2&amp;-1 \\\\[1.1ex] 0&amp;1&amp;k-4\\end{vmatrix} =0\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" 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-b265559f1f5505b8c40a89f0d69f0c10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle 2k-3 =0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"82\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u6211\u4eec\u89e3\u51b3\u4e86\u672a\u77e5\u7684\u95ee\u9898<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7cf6d2c84f82625cb8a795ee1394251f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" 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-f79b9d3960668149408038b9cb1d1e0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2k =3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-e67be6e218d206fe735f54a6125b3d2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k =}\\mathbf{\\cfrac{3}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"41\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p>\u6700\u540e\uff0c\u5982\u679c\u672c\u6587\u5bf9\u60a8\u6709\u7528\uff0c\u60a8\u53ef\u80fd\u8fd8\u5bf9\u5982\u4f55<a href=\"https:\/\/mathority.org\/cn\/\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u516c\u5f0f\u51e0\u4f55\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff08\u516c\u5f0f\uff09<\/a>\u611f\u5174\u8da3\uff0c\u56e0\u4e3a\u6709\u65f6\u5728\u89e3\u6790\u51e0\u4f55\u95ee\u9898\u4e2d\u6211\u4eec\u4f1a\u88ab\u95ee\u5230\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u662f\u591a\u5c11\u3002\u5728\u94fe\u63a5\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u975e\u5e38\u8be6\u7ec6\u7684\u89e3\u91ca\uff0c\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9\u4ee5\u53ca\u5982\u4f55\u77e5\u9053\u67d0\u4e9b\u70b9\u662f\u5426\u5171\u9762\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u793a\u4f8b\u5e76\u901a\u8fc7\u5df2\u89e3\u51b3\u7684\u5171\u9762 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e5%85%b1%e9%9d%a2%e6%88%96%e5%85%b1%e9%9d%a2%e7%82%b9%e7%a4%ba%e4%be%8b%e5%b7%b2%e8%a7%a3%e5%86%b3%e7%bb%83%e4%b9%a0\/\"> <span class=\"screen-reader-text\">\u5171\u9762\uff08\u6216\u5171\u9762\uff09\u70b9<\/span> \u67e5\u770b\u5168\u6587 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