{"id":56726,"date":"2014-09-16T05:34:26","date_gmt":"2014-09-15T21:34:26","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=56726"},"modified":"2021-10-06T16:15:15","modified_gmt":"2021-10-06T08:15:15","slug":"%e8%a1%8c%e5%88%97%e5%bc%8f%e7%9a%84%e6%80%a7%e8%b3%aa%ef%bc%88properties-of-determinant%ef%bc%89","status":"publish","type":"post","link":"http:\/\/localhost\/%e8%a1%8c%e5%88%97%e5%bc%8f%e7%9a%84%e6%80%a7%e8%b3%aa%ef%bc%88properties-of-determinant%ef%bc%89\/","title":{"rendered":"\u884c\u5217\u5f0f\u7684\u6027\u8cea"},"content":{"rendered":"

\u884c\u5217\u5f0f\u7684\u6027\u8cea\uff08Properties of Determinant\uff09<\/strong><\/span>
\n\u570b\u7acb\u81fa\u5357\u7b2c\u4e00\u9ad8\u7d1a\u4e2d\u5b78\u6797\u5009\u5104\u8001\u5e2b<\/strong><\/span><\/p>\n

\u9023\u7d50\uff1a\u884c\u5217\u5f0f\u7684\u5b9a\u7fa9<\/a><\/p>\n

\u5728\u672c\u6587\u4e2d\uff0c\u4e8c\u968e\u884c\u5217\u5f0f\u7684\u5b9a\u7fa9\u662f\u00a0\\(\\left| { \\begin{array}{*{20}{c}} {{a_{ 1}}}&{{b_{ 1}}}\\\\ {{a_{ 2}}}&{{b_{ 2}}} \\end{array} } \\right| = {a_{ 1}}{b_{ 2}} – {a_{ 2}}{b_{ 1}}\\)\uff0c<\/b><\/b><\/p>\n

\u4e09\u968e\u884c\u5217\u5f0f\u7684\u5b9a\u7fa9\u5247\u662f<\/b><\/p>\n

\\(\\left| { \\begin{array}{*{20}{c}} {{a_{ 1}}}&{{b_{ 1}}}&{{c_{ 1}}}\\\\ {{a_{ 2}}}&{{b_{ 2}}}&{{c_{ 2}}}\\\\ {{a_{ 3}}}&{{b_{ 3}}}&{{c_{ 3}}} \\end{array} } \\right| = {a_{ 1}} \\cdot \\left| { \\begin{array}{*{20}{c}} {{b_{ 2}}}&{{c_{ 2}}}\\\\ {{b_{ 3}}}&{{c_{ 3}}} \\end{array} } \\right| – {a_{ 2}} \\cdot \\left| { \\begin{array}{*{20}{c}} {{b_{ 1}}}&{{c_{ 1}}}\\\\ {{b_{ 3}}}&{{c_{ 3}}} \\end{array} } \\right| + {a_{ 3}} \\cdot \\left| { \\begin{array}{*{20}{c}} {{b_{ 1}}}&{{c_{ 1}}}\\\\ {{b_{ 2}}}&{{c_{ 2}}} \\end{array} } \\right| = {a_{ 1}}{b_{ 2}}{c_{ 3}} – {a_{ 1}}{b_{ 3}}{c_{ 2}} + {a_{ 2}}{b_{ 3}}{c_{ 1}} – {a_{ 2}}{b_{ 1}}{c_{ 3}} + {a_{ 3}}{b_{ 1}}{c_{ 2}} – {a_{ 3}}{b_{ 2}}{c_{ 1}}\\)\u00a0<\/b><\/b><\/p>\n

\u6211\u5011\u7a31\u76f4\u7684\u70ba\u884c\uff0c\u7531\u5de6\u800c\u53f3\u4f9d\u5e8f\u662f\u7b2c1\u884c\u3001\u7b2c2\u884c\u3001\u2026\uff1b\u7a31\u6a6b\u7684\u70ba\u5217\uff0c\u7531\u4e0a\u800c\u4e0b\u4f9d\u5e8f\u662f\u7b2c1\u5217\u3001\u7b2c2\u5217\u3001\u2026\u3002\u5229\u7528\u5b9a\u7fa9\uff0c\u5f88\u5bb9\u6613\u53ef\u4ee5\u63a8\u51fa\u4e0b\u5217\u4e8c\u968e\u8207\u4e09\u968e\u884c\u5217\u5f0f\u6027\u8cea\uff0c\u8b49\u660e\u5c31\u7565\u53bb\u3002<\/b><\/p>\n

    \n
  1. \u884c\u5217\u4e92\u63db\uff0c\u5176\u503c\u4e0d\u8b8a\uff1a
    \n    \"56726_eq1\"<\/a><\/li>\n
  2. \u4efb\u5169\u884c\u6216\u4efb\u5169\u5217\u5c0d\u8abf\uff0c\u5176\u503c\u8b8a\u865f\uff1a
    \n    \"56726_eq2\"<\/a>
    \n    \"56726_eq3\"<\/a>\"56726_eq4\"<\/a><\/li>\n
  3. \u4efb\u4e00\u884c\u6216\u4efb\u4e00\u5217\u4e58\u4e0a \\(k\\)\u00a0<\/i>\u500d\uff0c\u5176\u503c\u8b8a\u70ba \\(k\\)\u00a0<\/i>\u500d\u3002
    \n    \"56726_eq5\"<\/a>\"56726_eq6\"<\/a>\"56726_eq7\"<\/a>
    \n\u6b64\u6027\u8cea\u53ef\u89e3\u8b80\u6210\uff1a\u67d0\u4e00\u884c\u6216\u67d0\u4e00\u5217\u6709\u5171\u540c\u7684 \\(k\\) \u6642\uff0c\u53ef\u4ee5\u5c07 \\(k\\) \u63d0\u51fa\u4f86\uff0c\u4ea6\u53ef\u5c07\u4e58\u56de\u4efb\u4e00\u884c\u6216\u4efb\u4e00\u5217\u3002<\/li>\n
  4. \u4efb\u5169\u884c\u6216\u4efb\u5169\u5217\u6210\u6bd4\u4f8b\u6642\uff0c\u5176\u503c\u70ba \\(0\\)\uff1a
    \n    \"56726_eq8\"<\/a>
    \n    \"56726_eq9\"<\/a>
    \n    \"56726_eq10\"<\/a><\/li>\n
  5. \u53ef\u4f9d\u4efb\u4e00\u884c\u6216\u4efb\u4e00\u5217\u5c07\u4e00\u500b\u884c\u5217\u5f0f\u5206\u89e3\u6210\u5169\u500b\u884c\u5217\u5f0f\u7684\u548c\uff1b\u53cd\u4e4b\uff0c\u82e5\u5169\u500b\u884c\u5217\u5f0f\u53ea\u6709\u540c\u4e00\u884c\u6216\u540c\u4e00\u5217\u4e0d\u540c\uff0c\u5176\u9918\u7686\u76f8\u540c\uff0c\u90a3\u9ebc\uff0c\u9019\u5169\u500b\u884c\u5217\u5f0f\u53ef\u5408\u4f75\u6210\u4e00\u500b\u884c\u5217\u5f0f\uff1a
    \n    \"56726_eq11\"<\/a>
    \n    \"56726_eq12\"<\/a>
    \n    \"56726_eq13\"<\/a>
    \n    \"56726_eq14\"<\/a>
    \n\u4ee5    \"56726_eq15\"<\/a>\u70ba\u4f8b\u8aaa\u660e\uff0c
    \n\u5148\u5c07\u7b49\u865f\u5de6\u908a\u4f9d\u5b9a\u7fa9\u5c55\u958b\uff1a
    \n    \"56726_eq16\"<\/a><\/li>\n
  6. \u5c07\u4efb\u4e00\u884c\u7684 \\(k\\)\u00a0<\/i>\u500d\u52a0\u5230\u53e6\u4e00\u884c\uff0c\u5176\u503c\u4e0d\u8b8a\uff1b\u540c\u6a23\u5730\uff0c\u5c07\u4efb\u4e00\u5217\u7684 \\(k\\)\u00a0<\/i>\u500d\u52a0\u5230\u53e6\u4e00\u5217\uff0c\u5176\u503c\u4e0d\u8b8a\uff1a
    \n    \"56726_eq17\"<\/a>
    \n\u4ee5    \"56726_eq18\"<\/a>\u00a0\u70ba\u4f8b\u8aaa\u660e\uff1a
    \n    \"56726_eq19\"<\/a>
    \n\u63a5\u4f86\u9019\u500b\u6027\u8cea\u5728\u4e09\u968e\u4ee5\u4e0a\u7684\u884c\u5217\u5f0f\u624d\u6703\u7528\u5230\uff08\u5728\u4e8c\u968e\u884c\u5217\u5f0f\u4e5f\u53ef\u4ee5\u5beb\u51fa\u985e\u4f3c\u7684\u6027\u8cea\uff0c\u4f46\u5176\u7d50\u679c\u5c31\u662f\u5b9a\u7fa9\uff09<\/li>\n
  7. \u4e09\u968e\u884c\u5217\u5f0f\u53ef\u4ee5\u4f9d\u4efb\u4e00\u884c\u6216\u4efb\u4e00\u5217\u964d\u968e\u5c55\u958b\uff1a
    \n    \"56726_eq20\"<\/a>
    \n    \"56726_eq21\"<\/a>
    \n    \"56726_eq22\"<\/a>
    \n    \"56726_eq23\"<\/a>
    \n    \"56726_eq24\"<\/a>
    \n\u4ee5\u4f9d\u7b2c2\u884c\u964d\u968e\u5c55\u958b\u70ba\u4f8b\u8aaa\u660e\uff0c\u7531\u6027\u8cea(2)\u5f97    \"56726_eq25\"<\/a>\uff0c
    \n\u5c07    \"56726_eq26\"<\/a>\u4f9d\u5b9a\u7fa9\u5c55\u958b\uff1a\"56726_eq27\"<\/a>\uff0c\u6bcf\u4e00\u9805\u518d\u4e58\u4e0a\u8ca0\u865f\u5c31\u5f97\u5230\"56726_eq28\"<\/a>\u3002<\/li>\n<\/ol>\n

    \u4e0a\u8ff0\u9019\u4e9b\u6027\u8cea\uff0c\u5728\u56db\u968e\u4ee5\u4e0a\u7684\u884c\u5217\u5f0f\u4e5f\u90fd\u6210\u7acb\uff0c\u8b80\u8005\u4e0d\u59a8\u81ea\u884c\u9a57\u8b49\u770b\u770b\u3002\u73fe\u5728\uff0c\u8b93\u6211\u5011\u5229\u7528\u9019\u4e9b\u6027\u8cea\u518d\u91cd\u65b0\u8a08\u7b97\u524d\u6587\u3008\u884c\u5217\u5f0f\u7684\u5b9a\u7fa9\u3009\u4e2d\u7684\u4e09\u968e\u8207\u56db\u968e\u884c\u5217\u5f0f\u7684\u4f8b\u5b50\uff1a<\/p>\n

    \u4f8b<\/b>1<\/b>\uff1a<\/b>\u00a0\\(\\left| { \\begin{array}{*{20}{c}} 1&2&3\\\\ 4&5&6\\\\ 7&8&9 \\end{array} } \\right| = \\left| { \\begin{array}{*{20}{c}} 1&2&3\\\\ {4 – 1}&{5 – 2}&{6 – 3}\\\\ {7 – 1}&{8 – 2}&{9 – 3} \\end{array} } \\right| = \\left| { \\begin{array}{*{20}{c}} 1&2&3\\\\ 3&3&3\\\\ 6&6&6 \\end{array} } \\right| = 0\\)<\/b><\/p>\n

    \u4f8b2\uff1a \\(\\left| { \\begin{array}{*{20}{c}} 1&2&3&4\\\\ 5&6&7&8\\\\ 9&{10}&{11}&{12}\\\\ {13}&{14}&{15}&{16} \\end{array} } \\right| = \\left| { \\begin{array}{*{20}{c}} 1&2&3&4\\\\ {5 – 1}&{6 – 2}&{7 – 3}&{8 – 4}\\\\ {9 – 1}&{10 – 2}&{11 – 3}&{12 – 4}\\\\ {13}&{14}&{15}&{16} \\end{array} } \\right| = \\left| { \\begin{array}{*{20}{c}} 1&2&3&4\\\\ 4&4&4&4\\\\ 8&8&8&8\\\\ {13}&{14}&{15}&{16} \\end{array} } \\right| = 0\\)<\/b><\/p>\n

    \u5728\u8a08\u7b97\u884c\u5217\u5f0f\u4e4b\u503c\u6642\uff0c\u82e5\u80fd\u9069\u7576\u5730\u61c9\u7528\u6027\u8cea\uff0c\u6709\u6642\u5019\u5c31\u80fd\u5927\u5e45\u6e1b\u5c11\u8a08\u7b97\u91cf\u8207\u8907\u96dc\u5ea6\u3002\u96d6\u7136\u6027\u8cea\u6709\u597d\u5e7e\u500b\uff0c\u4f46\u719f\u80fd\u751f\u5de7\uff0c\u8b80\u8005\u591a\u627e\u5e7e\u500b\u4f8b\u5b50\u7df4\u7fd2\u5f8c\uff0c\u5c31\u80fd\u5145\u5206\u638c\u63e1\u9019\u4e9b\u6027\u8cea\u4e86\u3002\u6700\u5f8c\uff0c\u6211\u5011\u8981\u7528\u9019\u4e9b\u6027\u8cea\u4f86\u8b49\u660e\u3002<\/p>\n

    \"56726_eq29\"<\/a><\/p>\n

    \u8b49\u660e\u00a0\\(\\left| {\\begin{array}{*{20}{c}} 1&a&{{a^2}}\\\\ 1&b&{{b^2}}\\\\ 1&c&{{c^2}} \\end{array}} \\right| = (b – a)(c – a)(c – b)\\) \u6709\u5169\u500b\u76ee\u7684\uff0c\u9996\u5148\uff0c\u5b83\u662f\u884c\u5217\u5f0f\u4e2d\u540d\u6c23\u6700\u5927\u7684\u4e00\u500b\uff0c\u6709\u500b\u97ff\u5679\u5679\u7684\u540d\u5b57\u53eb\u300c\u8303\u5fb7\u8499\u884c\u5217\u5f0f\u300d\uff0c\u5b78\u4e86\u884c\u5217\u5f0f\u537b\u4e0d\u8a8d\u5f97\u5b83\uff0c\u6709\u9ede\u8aaa\u4e0d\u904e\u53bb\uff01<\/p>\n

    \u5176\u6b21\uff0c\u6211\u5011\u4e5f\u53ef\u4ee5\u7528\u300c\u66b4\u529b\u300d\u4f86\u8b49\u660e\u8303\u5fb7\u8499\u884c\u5217\u5f0f\uff0c\u5c31\u662f\u628a \\(\\left| {\\begin{array}{*{20}{c}} 1&a&{{a^2}}\\\\ 1&b&{{b^2}}\\\\ 1&c&{{c^2}} \\end{array}} \\right|\\) \u7684\u503c\uff08\u5c55\u958b\u5f0f\uff09\u4e58\u51fa\u4f86\uff0c\u518d\u628a\u4e58\u958b\uff0c\u5169\u76f8\u6bd4\u8f03\u5f8c\uff0c\u5c31\u77e5\u9053\u7b49\u865f\u6210\u7acb\u4e86\u3002\u9019\u500b\u300c\u66b4\u529b\u8b49\u6cd5\u300d\u5176\u5be6\u6709\u500b\u5927\u554f\u984c\uff0c\u5c31\u662f\u82e5\u6211\u5011\u4e0d\u77e5\u9053\u7b49\u865f\u53f3\u908a\u7684\u6a21\u6a23\uff0c\u90a3\u8a72\u600e\u9ebc\u8fa6\uff1f\u628a\\(\\left| {\\begin{array}{*{20}{c}} 1&a&{{a^2}}\\\\ 1&b&{{b^2}}\\\\ 1&c&{{c^2}} \\end{array}} \\right|\\) \u7684\u503c\uff08\u5c55\u958b\u5f0f\uff09\u505a\u56e0\u5f0f\u5206\u89e3\u55ce\uff1f\u9019\u96e3\u5ea6\u66f4\u9ad8\u4e86\uff01\u85c9\u7531\u6b64\u4f8b\uff0c\u6211\u5011\u77e5\u9053\u9069\u7576\u7684\u904b\u7528\u884c\u5217\u5f0f\u7684\u6027\u8cea\uff0c\u4e0d\u4f46\u53ef\u4ee5\u7c21\u5316\u8a08\u7b97\uff0c\u66f4\u53ef\u4ee5\u540c\u6642\u9054\u5230\u5206\u89e3\u7684\u6548\u679c\uff0c\u4e00\u8209\u5169\u5f97\uff0c\u4f55\u6a02\u800c\u4e0d\u70ba\uff1f<\/p>\n

    \u9023\u7d50\uff1a\u884c\u5217\u5f0f\u7684\u61c9\u7528<\/a><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u884c\u5217\u5f0f\u7684\u6027\u8cea\uff08Properties of Determinant\uff09 \u570b\u7acb\u81fa\u5357\u7b2c\u4e00\u9ad8\u7d1a\u4e2d\u5b78\u6797\u5009\u5104\u8001\u5e2b \u9023\u7d50\uff1a\u884c\u5217…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,232,231],"tags":[3493],"class_list":["post-56726","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math07-01","category-math07","tag-3493","loop-entry","cat-111","cat-232","cat-231","no-thumbnail"],"views":59146,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/56726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=56726"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/56726\/revisions"}],"predecessor-version":[{"id":86881,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/56726\/revisions\/86881"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=56726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=56726"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=56726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}