{"id":231,"date":"2023-07-10T20:13:15","date_gmt":"2023-07-10T20:13:15","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e9%87%8d%e5%90%88%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%92%8c%e7%a4%ba%e4%be%8b\/"},"modified":"2023-07-10T20:13:15","modified_gmt":"2023-07-10T20:13:15","slug":"%e9%87%8d%e5%90%88%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%92%8c%e7%a4%ba%e4%be%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e9%87%8d%e5%90%88%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%92%8c%e7%a4%ba%e4%be%8b\/","title":{"rendered":"\u91cd\u5408\u7ebf"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u91cd\u5408\u7ebf\u7684\u6240\u6709\u4fe1\u606f\uff1a\u5b83\u4eec\u7684\u542b\u4e49\u3001\u5982\u4f55\u786e\u5b9a\u4e24\u6761\u7ebf\u662f\u5426\u91cd\u5408\u3001\u5b83\u4eec\u7684\u5c5e\u6027\u7b49\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u91cd\u5408\u7ebf\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-dos-rectas-coincidentes\"><\/span>\u4ec0\u4e48\u662f\u4e24\u6761\u91cd\u5408\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e24\u6761\u91cd\u5408\u7ebf\u662f\u5177\u6709\u6240\u6709\u516c\u5171\u70b9\u7684\u4e24\u6761\u7ebf\u3002<\/strong>\u56e0\u6b64\uff0c\u4e24\u6761\u91cd\u5408\u7ebf\u662f\u5b8c\u5168\u76f8\u540c\u7684\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u4e0b\u9762\u7ed8\u5236\u4e86\u4e24\u6761\u91cd\u5408\u7ebf\uff0c\u4f46\u60a8\u53ea\u80fd\u770b\u5230\u4e00\u6761\uff0c\u56e0\u4e3a\u5b83\u4eec\u91cd\u53e0\uff08\u5b83\u4eec\u76f8\u7b49\uff09\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\/angle-coincident-lignes.webp\" alt=\"\" class=\"wp-image-1646\" width=\"197\" height=\"175\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e24\u6761\u91cd\u5408\u7ebf\u59cb\u7ec8\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\uff0c\u56e0\u6b64\u5728\u51e0\u4f55\u4e0a\u5b83\u4eec\u5f62\u6210 0\u00b0 \u7684\u89d2\u5ea6\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u5728\u5e73\u9762\u4e2d\uff0c\u4e24\u6761\u7ebf\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\u6982\u5ff5\u6709 4 \u79cd\u53ef\u80fd\u6027\uff1a\u4e24\u6761\u7ebf\u53ef\u4ee5\u91cd\u5408\u3001<a href=\"https:\/\/mathority.org\/cn\/\u5e73\u884c\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50\/\">\u5e73\u884c<\/a>\u3001<a href=\"https:\/\/mathority.org\/cn\/\u76f8\u4ea4\u7ebf\u793a\u4f8b\/\">\u5272\u7ebf<\/a>\u548c<a href=\"https:\/\/mathority.org\/cn\/\u5782\u76f4\u7ebf\u7684\u5b9a\u4e49\u548c\u4f8b\u5b50-\u5782\u76f4\u5ea6\/\">\u5782\u76f4<\/a>\u3002\u5982\u679c\u9700\u8981\uff0c\u60a8\u53ef\u4ee5\u5728\u8fd9 3 \u4e2a\u94fe\u63a5\u4e2d\u67e5\u770b\u6bcf\u79cd\u7ebf\u578b\u7684\u542b\u4e49\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u533a\u522b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-saber-si-dos-rectas-son-coincidentes\"><\/span>\u4f60\u600e\u4e48\u77e5\u9053\u4e24\u6761\u7ebf\u662f\u5426\u91cd\u5408\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u77e5\u9053\u4e24\u6761\u7ebf\u4f55\u65f6\u91cd\u5408\u53d6\u51b3\u4e8e\u60a8\u662f\u4f7f\u7528\u4e24\u4e2a\u5750\u6807\uff08\u5728 R2 \u4e2d\uff09\u8fd8\u662f\u4f7f\u7528\u4e09\u4e2a\u5750\u6807\uff08\u5728 R3 \u4e2d\uff09\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-dos-rectas-coincidentes-en-el-plano\"><\/span>\u786e\u5b9a\u5e73\u9762\u5185\u4e24\u6761\u91cd\u5408\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5f53\u6211\u4eec\u5728\u4e8c\u7ef4 (2D) \u7a7a\u95f4\u4e2d\u64cd\u4f5c\u65f6\uff0c\u5f88\u5bb9\u6613\u770b\u51fa\u4e24\u6761\u76f4\u7ebf\u4f55\u65f6\u91cd\u5408\u4ee5\u53ca\u4f55\u65f6\u5b83\u4eec\u4e0d\u662f\u7531\u76f4\u7ebf\u7684<strong>\u9690\u5f0f\u65b9\u7a0b<\/strong>\u6216<strong><strong>\u663e\u5f0f<\/strong>\u65b9\u7a0b<\/strong>\u4ea7\u751f\u3002<\/p>\n<p>\u9664\u4e86\u8fd9\u4e24\u79cd\u65b9\u6cd5\u4e4b\u5916\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u6c42\u89e3\u4e24\u6761\u76f4\u7ebf\u65b9\u7a0b\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\u6765\u68c0\u67e5\u4e24\u6761\u76f4\u7ebf\u662f\u5426\u91cd\u5408\uff08\u5982\u679c\u8be5\u65b9\u7a0b\u7ec4\u7ed9\u51fa\u65e0\u9650\u4e2a\u89e3\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u91cd\u5408\uff09\u3002\u4f46\u8fd9\u4e2a\u8fc7\u7a0b\u6bd4\u8f83\u590d\u6742\u4e14\u8017\u65f6\uff0c\u56e0\u6b64\u6211\u4eec\u4e0d\u4f1a\u8be6\u7ec6\u89e3\u91ca\u5b83\uff0c\u56e0\u4e3a\u6700\u597d\u4ece\u9690\u5f0f\u65b9\u7a0b\u6216\u663e\u5f0f\u65b9\u7a0b\u7684\u7cfb\u6570\u6765\u8fdb\u884c\u3002 <\/p>\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"a-partir-de-la-ecuacion-implicita-o-general-de-la-recta\"><\/span>\u4ece\u76f4\u7ebf\u7684\u9690\u5f0f\uff08\u6216\u4e00\u822c\uff09\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u5224\u65ad\u4e24\u6761\u76f4\u7ebf\u662f\u5426\u91cd\u5408\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u76f4\u7ebf\u7684\u9690\u5f0f\u65b9\u7a0b\uff0c\u4e5f\u79f0\u4e3a\u4e00\u822c\u65b9\u7a0b\u6216\u7b1b\u5361\u5c14\u65b9\u7a0b\u3002<\/p>\n<p>\u8be5\u76f4\u7ebf\u7684\u9690\u5f0f\u65b9\u7a0b\u5bf9\u5e94\u4e8e\u4ee5\u4e0b\u8868\u8fbe\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-02f4d03229cc8bd79a81b676a8132f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u597d\u5427<strong>\uff0c\u5982\u679c\u4e24\u6761\u7ebf\u5177\u6709\u4e09\u4e2a\u6bd4\u4f8b\u7cfb\u6570\uff08A\u3001B \u548c C\uff09<\/strong> \uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u91cd\u5408\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-ce8e0c71142b89e0985aa730b40f15db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ Ax+By+C=0 \\qquad \\qquad s: \\ A'x+B'y+C'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"417\" 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-38af209a728e212f09684571275aa91e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{A}{A'} = \\cfrac{B}{B'}= \\cfrac{C}{C'} \\quad \\longrightarrow \\quad \\bm{r} \\text{ y } \\bm{s} \\text{ son coincidentes}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"349\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4e24\u884c\u5339\u914d\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-67280ad255ed8320fb340756b25bed0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 4x+6y-2=0 \\qquad \\qquad s: \\ 2x+3y-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"373\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u5b83\u4eec\u91cd\u5408\u662f\u56e0\u4e3a\u53c2\u6570 A\u3001B \u548c C \u5f7c\u6b64\u6210\u6bd4\u4f8b\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-96271c1670f39bd2f0b064b928e5bbf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{2} = \\cfrac{6}{3}= \\cfrac{-2}{-1}= 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"131\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"a-partir-de-la-ecuacion-explicita-de-la-recta\"><\/span>\u4ece\u76f4\u7ebf\u7684\u663e\u5f0f\u65b9\u7a0b<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>\u786e\u5b9a\u4e24\u6761\u76f4\u7ebf\u662f\u5426\u771f\u6b63\u91cd\u5408\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528\u76f4\u7ebf\u7684\u663e\u5f0f\u65b9\u7a0b\u3002\u56de\u60f3\u4e00\u4e0b\uff0c\u8be5\u76f4\u7ebf\u7684\u663e\u5f0f\u65b9\u7a0b\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-8e4adcc4368f6296906b6231bf17a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p><strong>\u5982\u679c\u4e24\u6761\u7ebf\u5177\u6709\u76f8\u540c\u7684\u659c\u7387<\/strong>\uff08\u7cfb\u6570 m\uff09<strong>\u548c\u539f\u70b9\u5904\u76f8\u540c\u7684\u7eb5\u5750\u6807<\/strong>\uff08\u7cfb\u6570 n\uff09\uff0c\u5219\u5b83\u4eec\u662f\u4e24\u6761\u7ebf\u7684\u7ec4\u5408\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-118d5497956dca1ee066f6df259638a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ y=m_rx+n_r \\qquad \\qquad s: \\ y=m_sx+n_s\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"339\" 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-31b5e5f16e9b8d4a399ff746d166ec46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{c} m_r = m_s \\\\[2ex] n_r=n_s \\end{array} \\right\\} \\longrightarrow \\ \\bm{r} \\text{ y } \\bm{s} \\text{ son  coincidentes}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"306\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u4ee5\u4e0b\u4e24\u6761\u7ebf\u662f\u76f8\u540c\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u6700\u521d\u5177\u6709\u76f8\u540c\u7684\u659c\u7387\u548c\u5750\u6807\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-f866703bb2cd8358ae2c77517f113dec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ y=3x-1 \\qquad \\qquad s: \\ y=3x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"293\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u5e94\u8be5\u6ce8\u610f\u7684\u662f\uff0c\u5982\u679c\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u659c\u7387\u4f46\u5728\u539f\u70b9\u5904\u7684\u987a\u5e8f\u4e0d\u540c\uff0c\u90a3\u4e48\u5b83\u4eec\u5c06\u662f\u5e73\u884c\u7684\u800c\u4e0d\u662f\u91cd\u5408\u7684\u7ebf\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6b63\u5982\u60a8\u5728\u793a\u4f8b\u4e2d\u770b\u5230\u7684\uff0c\u4e24\u6761\u91cd\u5408\u7ebf\u5177\u6709\u76f8\u540c\u7684\u663e\u5f0f\u65b9\u7a0b\u3002\u8fd9\u9002\u7528\u4e8e\u4efb\u4f55\u7c7b\u578b\u7684\u76f4\u7ebf\u65b9\u7a0b\uff1a\u5982\u679c\u4e24\u6761\u76f4\u7ebf\u5728\u65b9\u7a0b\u4e2d\u91cd\u5408\uff0c\u5219\u610f\u5473\u7740\u5b83\u4eec\u91cd\u5408\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-dos-rectas-coincidentes-en-el-espacio\"><\/span>\u5728\u7a7a\u95f4\u4e2d\u627e\u5230\u4e24\u6761\u91cd\u5408\u7ebf<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5728\u7a7a\u95f4\uff08R3\uff09\u4e2d\u8bc6\u522b\u4e24\u6761\u91cd\u5408\u7ebf\u4e0e\u5728\u7b1b\u5361\u5c14\u5e73\u9762\uff08R2\uff09\u4e2d\u8bc6\u522b\u4e24\u6761\u91cd\u5408\u7ebf\u4e0d\u540c\uff0c\u56e0\u4e3a\u8ba1\u7b97\u5fc5\u987b\u591a\u4e00\u4e2a\u5750\u6807\u3002\u90a3\u4e48\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\uff1a<\/p>\n<p>\u7ed9\u5b9a\u7a7a\u95f4\u4e2d\u4e24\u6761\u4e0d\u540c\u76f4\u7ebf\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-a7ed891adcd2a9eb85e22808c151a857_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} A_1x+B_1y+C_1z+D_1=0 \\\\[2ex]A_2x+B_2y+C_2z+D_2=0 \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} A_1'x+B_1'y+C_1'z+D_1'=0 \\\\[2ex]A_2'x+B_2'y+C_2'z+D_2'=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"601\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4ee4 M \u548c M&#8217; \u4e3a\u7531\u5404\u884c\u7cfb\u6570\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-cb73091f41e0751855a8e1b7e73ac4d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle M=\\begin{pmatrix} A_1&amp;B_1&amp;C_1\\\\[1.1ex]A_2&amp;B_2&amp;C_2 \\\\[1.1ex]A_1'&amp;B_1'&amp;C_1'\\\\[1.1ex]A_2'&amp;B_2'&amp;C_2' \\end{pmatrix}\\qquad \\qquad M'=\\begin{pmatrix} A_1&amp;B_1&amp;C_1&amp;D_1 \\\\[1.1ex]A_2&amp;B_2&amp;C_2&amp;D_2 \\\\[1.1ex]A_1'&amp;B_1'&amp;C_1'&amp;D_1'\\\\[1.1ex]A_2'&amp;B_2'&amp;C_2'&amp;D_2' \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"450\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\uff0c<strong>\u5982\u679c\u77e9\u9635 M \u548c M&#8217; \u7684\u79e9\u7b49\u4e8e 2\uff0c\u5219\u4e24\u6761\u7ebf\u91cd\u5408\u3002<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ec4a947fabe774c5f2e3bbfd05ddcd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(M)=rg(M') = 2 \\ \\longrightarrow \\ \\bm{r} \\text{ y } \\bm{s} \\text{ son coincidentes}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"381\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u6765\u770b\u4e00\u4e2a\u7a7a\u95f4\u91cd\u5408\u7ebf\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li>\u5224\u65ad\u4ee5\u4e0b\u4e24\u884c\u662f\u5426\u5339\u914d\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-8a81fab3c2adb66dc44c4c31384838ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x+2y+z+3=0 \\\\[2ex]3x+4y+z+8=0 \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} x-z+2=0 \\\\[2ex]2y+2z+1=0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5404\u884c\u7cfb\u6570\u7684\u77e9\u9635M\u548c\u6269\u5c55\u77e9\u9635M&#8217;\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-4451bc436023267251b927f54717d02d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle M=\\begin{pmatrix} 1&amp;2&amp;1 \\\\[1.1ex]3&amp;4&amp;1 \\\\[1.1ex]1&amp;0&amp;-1\\\\[1.1ex]0&amp;2&amp;2\\end{pmatrix}\\qquad \\qquad M'=\\begin{pmatrix} 1&amp;2&amp;1&amp;3 \\\\[1.1ex]3&amp;4&amp;1&amp;8 \\\\[1.1ex]1&amp;0&amp;-1&amp;2\\\\[1.1ex]0&amp;2&amp;2&amp;1\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"392\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4e00\u65e6\u6211\u4eec\u6784\u5efa\u4e86\u4e24\u4e2a\u77e9\u9635\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u6bcf\u4e2a\u77e9\u9635\u7684\u8303\u56f4\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-a9ea6ecf0646ec24eef5f5aee77cced9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(M)=2 \\qquad \\qquad rg(M') = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4e24\u4e2a\u77e9\u9635\u7684\u79e9\u76f8\u7b49\uff0c\u800c\u4e14\u5b83\u4eec\u7684\u503c\u4e3a 2\u3002<strong>\u56e0\u6b64\uff0c\u4e24\u6761\u7ebf\u662f\u6df7\u6dc6\u7684\u3002<\/strong> <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3ec4a947fabe774c5f2e3bbfd05ddcd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(M)=rg(M') = 2 \\ \\longrightarrow \\ \\bm{r} \\text{ y } \\bm{s} \\text{ son coincidentes}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"381\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-rectas-coincidentes\"><\/span>\u91cd\u5408\u7ebf\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u91cd\u5408\u7ebf\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul>\n<li>\u4e24\u6761\u91cd\u5408\u7ebf\u7684\u65b9\u5411\u77e2\u91cf\uff08\u6307\u793a\u7ebf\u65b9\u5411\u7684\u77e2\u91cf\uff09\u6210\u6bd4\u4f8b\uff0c\u56e0\u6b64\u7ebf\u6027\u76f8\u5173\u3002\u5e73\u884c\u7ebf\u4e5f\u6709\u8fd9\u4e2a\u6027\u8d28\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u540c\u6837\uff0c\u4e24\u6761\u91cd\u5408\u7ebf\u7684\u65b9\u5411\u77e2\u91cf\u5177\u6709\u76f8\u540c\u7684\u65b9\u5411\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4e24\u6761\u91cd\u5408\u7ebf\u5728\u56fe\u5f62\u4e0a\u7528\u540c\u4e00\u6761\u7ebf\u8868\u793a\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u4e24\u6761\u91cd\u5408\u7ebf\u90fd\u6709\u5171\u540c\u70b9\u3002\u56e0\u6b64\uff0c\u4e0e\u8f74\u7684\u4ea4\u70b9\u662f\u76f8\u540c\u7684\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u663e\u7136\uff0c\u4e24\u6761\u91cd\u5408\u7ebf\u662f\u5171\u9762\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u4eec\u5305\u542b\u5728\u540c\u4e00\u5e73\u9762\u5185\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u6709\u5173\u91cd\u5408\u7ebf\u7684\u6240\u6709\u4fe1\u606f\uff1a\u5b83\u4eec\u7684\u542b\u4e49\u3001\u5982\u4f55\u786e\u5b9a\u4e24\u6761\u7ebf\u662f\u5426\u91cd\u5408\u3001\u5b83\u4eec\u7684\u5c5e\u6027\u7b49\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u91cd\u5408 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e9%87%8d%e5%90%88%e7%ba%bf%e5%ae%9a%e4%b9%89%e5%92%8c%e7%a4%ba%e4%be%8b\/\"> <span class=\"screen-reader-text\">\u91cd\u5408\u7ebf<\/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":[15],"tags":[],"class_list":["post-231","post","type-post","status-publish","format-standard","hentry","category-15"],"yoast_head":"<!-- This site is optimized 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