习题课：n阶行列式的计算 行列式课后习题
\u5168\u56fd2008\u5e747\u6708\u9ad8\u7b49\u6559\u80b2\u81ea\u5b66\u8003\u8bd5,<<\u7ebf\u6027\u4ee3\u6570(\u7ecf\u7ba1\u7c7b)>>\u8bd5\u9898\u53ca\u7b54\u6848,\u8bfe\u7a0b\u4ee3\u7801\uff1a4184\u6709\u4e00\u4e9b\u8bfe\u5802\u7b14\u8bb0\uff0c \u4e0d\u77e5\u9053\u5bf9\u4f60\u6709\u6ca1\u6709\u7528\uff0c\u8fd8\u662f\u53d1\u7ed9\u4f60\u5427
\u7b2c\u4e00\u7ae0 \u884c\u5217\u5f0f
\u7ebf\u6027\u4ee3\u6570\u5b66\u7684\u6838\u5fc3\u5185\u5bb9\u662f\uff1a\u7814\u7a76\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u7684\u5b58\u5728\u6761\u4ef6\u3001\u89e3\u7684\u7ed3\u6784\u4ee5\u53ca\u89e3\u7684\u6c42\u6cd5\u3002\u6240\u7528\u7684\u57fa\u672c\u5de5\u5177\u662f\u77e9\u9635\uff0c\u800c\u884c\u5217\u5f0f\u662f\u7814\u7a76\u77e9\u9635\u7684\u5f88\u6709\u6548\u7684\u5de5\u5177\u4e4b\u4e00\u3002\u884c\u5217\u5f0f\u4f5c\u4e3a\u4e00\u79cd\u6570\u5b66\u5de5\u5177\u4e0d\u4f46\u5728\u672c\u8bfe\u7a0b\u4e2d\u6781\u5176\u91cd\u8981\uff0c\u800c\u4e14\u5728\u5176\u4ed6\u6570\u5b66\u5b66\u79d1\u3001\u4e43\u81f3\u5728\u5176\u4ed6\u8bb8\u591a\u5b66\u79d1\uff08\u4f8b\u5982\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u7ba1\u7406\u5b66\u7b49\uff09\u90fd\u662f\u5fc5\u4e0d\u53ef\u5c11\u7684\u3002
1.1 \u884c\u5217\u5f0f\u7684\u5b9a\u4e49
\uff08\u4e00\uff09\u4e00\u9636\u3001\u4e8c\u9636\u3001\u4e09\u9636\u884c\u5217\u5f0f\u7684\u5b9a\u4e49
\uff081\uff09\u5b9a\u4e49\uff1a\u7b26\u53f7 \u53eb\u4e00\u9636\u884c\u5217\u5f0f\uff0c\u5b83\u662f\u4e00\u4e2a\u6570\uff0c\u5176\u5927\u5c0f\u89c4\u5b9a\u4e3a\uff1a \u3002
\u6ce8\u610f\uff1a\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0c\u7b26\u53f7 \u4e0d\u662f\u7edd\u5bf9\u503c\u3002
\u4f8b\u5982 \uff0c\u4e14 \uff1b
\uff082\uff09\u5b9a\u4e49\uff1a\u7b26\u53f7 \u53eb\u4e8c\u9636\u884c\u5217\u5f0f\uff0c\u5b83\u4e5f\u662f\u4e00\u4e2a\u6570\uff0c\u5176\u5927\u5c0f\u89c4\u5b9a\u4e3a\uff1a \u6240\u4ee5\u4e8c\u9636\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u4e24\u4e2a\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6570\u7684\u79ef\u4e4b\u5dee\u3002
\u4f8b\u5982
\uff083\uff09\u7b26\u53f7 \u53eb\u4e09\u9636\u884c\u5217\u5f0f\uff0c\u5b83\u4e5f\u662f\u4e00\u4e2a\u6570\uff0c\u5176\u5927\u5c0f\u89c4\u5b9a\u4e3a
\u4f8b\u5982 =0
\u4e09\u9636\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u6bd4\u8f83\u590d\u6742\uff0c\u4e3a\u4e86\u5e2e\u52a9\u5927\u5bb6\u638c\u63e1\u4e09\u9636\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u516c\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u4e0b\u9762\u7684\u5bf9\u89d2\u7ebf\u6cd5\u8bb0\u5fc6
\u65b9\u6cd5\u662f\uff1a\u5728\u5df2\u7ed9\u884c\u5217\u5f0f\u53f3\u8fb9\u6dfb\u52a0\u5df2\u7ed9\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u5217\u3001\u7b2c\u4e8c\u5217\u3002\u6211\u4eec\u628a\u884c\u5217\u5f0f\u5de6\u4e0a\u89d2\u5230\u53f3\u4e0b\u89d2\u7684\u5bf9\u89d2\u7ebf\u53eb\u4e3b\u5bf9\u89d2\u7ebf\uff0c\u628a\u53f3\u4e0a\u89d2\u5230\u5de6\u4e0b\u89d2\u7684\u5bf9\u89d2\u7ebf\u53eb\u6b21\u5bf9\u89d2\u7ebf\uff0c\u8fd9\u65f6\uff0c\u4e09\u9636\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u4e3b\u5bf9\u89d2\u7ebf\u7684\u4e09\u4e2a\u6570\u7684\u79ef\u4e0e\u548c\u4e3b\u5bf9\u89d2\u7ebf\u5e73\u884c\u7684\u7ebf\u4e0a\u7684\u4e09\u4e2a\u6570\u7684\u79ef\u4e4b\u548c\u51cf\u53bb\u6b21\u5bf9\u89d2\u7ebf\u4e09\u4e2a\u6570\u7684\u79ef\u4e0e\u6b21\u5bf9\u89d2\u7ebf\u7684\u5e73\u884c\u7ebf\u4e0a\u6570\u7684\u79ef\u4e4b\u548c\u3002
\u4f8b\u5982\uff1a
\uff081\uff09
=1\u00d75\u00d79+2\u00d76\u00d77+3\u00d74\u00d78-3\u00d75\u00d77-1\u00d76\u00d78-2\u00d74\u00d79=0
\uff082\uff09
\uff083\uff09
\uff082\uff09\u548c\uff083\uff09\u53eb\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\uff0c\u5176\u4e2d\uff082\uff09\u53eb\u4e0a\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\uff0c\uff083\uff09\u53eb\u4e0b\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\uff0c\u7531\uff082\uff09\uff083\uff09\u53ef\u89c1\uff0c\u5728\u4e09\u9636\u884c\u5217\u5f0f\u4e2d\uff0c\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\u7684\u503c\u4e3a\u4e3b\u5bf9\u89d2\u7ebf\u7684\u4e09\u4e2a\u6570\u4e4b\u79ef\uff0c\u5176\u4f59\u4e94\u9879\u90fd\u662f0\uff0c\u4f8b\u5982
\u4f8b1 a\u4e3a\u4f55\u503c\u65f6\uff0c
[\u7b54\u7591\u7f16\u53f710010101\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3 \u56e0\u4e3a
\u6240\u4ee58-3a=0\uff0c \u65f6
\u4f8b2 \u5f53x\u53d6\u4f55\u503c\u65f6\uff0c
[\u7b54\u7591\u7f16\u53f710010102\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a
\u89e3\u5f97 0<x<9
\u6240\u4ee5\u5f530<x<9\u65f6\uff0c\u6240\u7ed9\u884c\u5217\u5f0f\u5927\u4e8e0\u3002
\uff08\u4e8c\uff09n\u9636\u884c\u5217\u5f0f
\u7b26\u53f7\uff1a
\u5b83\u7531n\u884c\u3001n\u5217\u5143\u7d20\uff08\u5171 \u4e2a\u5143\u7d20\uff09\u7ec4\u6210\uff0c\u79f0\u4e4b\u4e3an\u9636\u884c\u5217\u5f0f\u3002\u5176\u4e2d\uff0c\u6bcf\u4e00\u4e2a\u6570 \u79f0\u4e3a\u884c\u5217\u5f0f\u7684\u4e00\u4e2a\u5143\u7d20\uff0c\u5b83\u7684\u524d\u4e00\u4e2a\u4e0b\u6807i\u79f0\u4e3a\u884c\u6807\uff0c\u5b83\u8868\u793a\u8fd9\u4e2a\u6570 \u5728\u7b2ci\u884c\u4e0a\uff1b\u540e\u4e00\u4e2a\u4e0b\u6807j \u79f0\u4e3a\u5217\u6807\uff0c\u5b83\u8868\u793a\u8fd9\u4e2a\u6570 \u5728\u7b2cj\u5217\u4e0a\u3002\u6240\u4ee5 \u5728\u884c\u5217\u5f0f\u7684\u7b2ci\u884c\u548c\u7b2cj\u5217\u7684\u4ea4\u53c9\u4f4d\u7f6e\u4e0a\u3002\u4e3a\u53d9\u8ff0\u65b9\u4fbf\u8d77\u89c1\uff0c\u6211\u4eec\u7528(i,j)\u8868\u793a\u8fd9\u4e2a\u4f4d\u7f6e\u3002n\u9636\u884c\u5217\u5f0f \u901a\u5e38\u4e5f\u7b80\u8bb0\u4f5c \u3002
n\u9636\u884c\u5217\u5f0f \u4e5f\u662f\u4e00\u4e2a\u6570\uff0c\u81f3\u4e8e\u5b83\u7684\u503c\u7684\u8ba1\u7b97\u65b9\u6cd5\u9700\u8981\u5f15\u5165\u4e0b\u9762\u4e24\u4e2a\u6982\u5ff5\u3002
\uff081\uff09\u5728n\u9636\u884c\u5217\u5f0f \u4e2d\uff0c\u5212\u53bb\u5b83\u7684\u7b2ci\u884c\u548c\u7b2cj\u5217\uff0c\u4f59\u4e0b\u7684\u6570\u6309\u7167\u539f\u6765\u76f8\u5bf9\u987a\u5e8f\u7ec4\u6210\u7684\u4e00\u4e2a(n-1)\u9636\u884c\u5217\u5f0f\u53eb\u5143\u7d20 \u7684\u4f59\u5b50\u5f0f\uff0c\u8bb0\u4f5c
\u4f8b\u5982\uff0c\u5728\u4e09\u9636\u884c\u5217\u5f0f
\u4e2d\uff0c \u7684\u4f59\u5b50\u5f0f \u8868\u793a\u5c06\u4e09\u9636\u884c\u5217\u5f0f \u5212\u53bb\u7b2c1\u884c\u548c\u7b2c1\u5217\u540e\uff0c\u4f59\u4e0b\u7684\u6570\u6309\u7167\u76f8\u5bf9\u4f4d\u7f6e\u7ec4\u6210\u7684\u4e8c\u9636\u884c\u5217\u5f0f\uff0c\u6240\u4ee5
\u76f8\u4f3c\u5730\uff0c \u7684\u4f59\u5b50\u5f0f \u8868\u793a\u5c06\u4e09\u9636\u884c\u5217\u5f0f \u5212\u53bb\u7b2c\u4e8c\u884c\u548c\u7b2c\u4e09\u5217\u540e\uff0c\u4f59\u4e0b\u7684\u6570\u7ec4\u6210\u7684\u4e8c\u9636\u884c\u5217\u5f0f\u3002\u6240\u4ee5
\u4f8b1 \u82e5 \uff0c\u6c42\uff1a
\uff081\uff09
[\u7b54\u7591\u7f16\u53f710010103\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff082\uff09
[\u7b54\u7591\u7f16\u53f710010104\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff083\uff09
[\u7b54\u7591\u7f16\u53f710010105\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff084\uff09
[\u7b54\u7591\u7f16\u53f710010106\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff081\uff09
\uff082\uff09
\uff083\uff09
\uff084\uff09
\uff082\uff09\u7b26\u53f7 \u53eb\u5143\u7d20 \u7684\u4ee3\u6570\u4f59\u5b50\u5f0f
\u5b9a\u4e49\uff1a
\u4f8b2 \u6c42\u4f8b1\u4e2d \u7684\u4ee3\u6570\u4f59\u5b50\u5f0f
\uff081\uff09
[\u7b54\u7591\u7f16\u53f710010107\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff082\uff09
[\u7b54\u7591\u7f16\u53f710010108\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff083\uff09
[\u7b54\u7591\u7f16\u53f710010109\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\uff084\uff09
[\u7b54\u7591\u7f16\u53f710010110\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\uff081\uff09
\uff082\uff09
\uff083\uff09
\uff084\uff09
\u4f8b3 \u82e5
\u8ba1\u7b97
[\u7b54\u7591\u7f16\u53f710010111\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a
\u7531\u4e8e
\u4e0e\u4f8b3\u7684\u7ed3\u679c\u6bd4\u8f83\uff0c\u53d1\u73b0
\u8fd9\u4e00\u7ed3\u679c\u8bf4\u660e\uff1a\u4e09\u9636\u884c\u5217\u5f0f \u7b49\u4e8e\u5b83\u7684\u7b2c\u4e00\u5217\u7684\u5143\u7d20\u4e0e\u5bf9\u5e94\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u7684\u79ef\u7684\u548c\uff0c\u8fd9\u4e00\u7ed3\u679c\u53ef\u4ee5\u63a8\u5e7f\u5230n\u9636\u884c\u5217\u5f0f\u4f5c\u4e3a\u5b9a\u4e49\u3002
\u5b9a\u4e49\uff1an\u9636\u884c\u5217\u5f0f
\u5373\u89c4\u5b9an\u9636\u884c\u5217\u5f0f \u7684\u503c\u4e3a\u5b83\u7684\u7b2c\u4e00\u5217\u7684\u5143\u7d20\u4e0e\u76f8\u5e94\u4ee3\u6570\u4f59\u5b50\u5f0f\u7684\u79ef\u7684\u548c\uff0c\u4e0a\u9762\u7ed3\u679c\u4e2d\u56e0\u4e3a
\u6240\u4ee5\u6709
\u7279\u522b\u60c5\u5f62
\u4f8b4 \u8ba1\u7b97\u4e0b\u5217\u884c\u5217\u5f0f
\uff081\uff09
[\u7b54\u7591\u7f16\u53f710010112\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u7531\u672c\u4f8b\u53ef\u89c1\u56db\u9636\u4e0a\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\u7684\u503c\u4e5f\u7b49\u4e8e\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u5404\u6570\u4e4b\u79ef
\uff082\uff09
[\u7b54\u7591\u7f16\u53f710010113\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u53ef\u89c1\u4e94\u9636\u4e0a\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\u7684\u503c\u4ecd\u7b49\u4e8e\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u5404\u6570\u4e4b\u79ef
\u4e00\u822c\u5730\u53ef\u63a8\u5f97
\u5373\u4efb\u610fn\u9636\u4e0a\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u5404\u6570\u4e4b\u79ef
\u540c\u7406\u6709
1.2 \u884c\u5217\u5f0f\u6309\u884c\uff08\u5217\uff09\u5c55\u5f00
\u57281.1\u8282\u8bb2n\u9636\u884c\u5217\u5f0f\u7684\u5c55\u5f00\u65f6\uff0c\u662f\u628a \u6309\u5176\u7b2c\u4e00\u5217\u5c55\u5f00\u800c\u9010\u6b65\u628a\u884c\u5217\u5f0f\u7684\u9636\u6570\u964d\u4f4e\u4ee5\u540e\uff0c\u518d\u6c42\u51fa\u5176\u503c\u3002\u5b9e\u9645\u4e0a\uff0c\u884c\u5217\u5f0f\u53ef\u4ee5\u6309\u5176\u4efb\u610f\u4e00\u884c\u6216\u6309\u5176\u4efb\u610f\u4e00\u5217\u5c55\u5f00\u6765\u6c42\u51fa\u5b83\u7684\u503c\u3002
\u73b0\u5728\u7ed9\u51fa\u4e0b\u9762\u7684\u91cd\u8981\u5b9a\u7406\uff0c\u5176\u8bc1\u660e\u4ece\u7565\u3002
\u5b9a\u74061.2.1\uff08\u884c\u5217\u5f0f\u5c55\u5f00\u5b9a\u7406\uff09n\u9636\u884c\u5217\u5f0f \u7b49\u4e8e\u5b83\u7684\u4efb\u610f\u4e00\u884c\uff08\u5217\uff09\u7684\u5404\u5143\u7d20\u4e0e\u5176\u5bf9\u5e94\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u7684\u4e58\u79ef\u4e4b\u548c\uff0c\u5373
\uff08i=1,2,\u2026,n\uff09 \uff081.8\uff09
\u6216 \uff08j=1,2,\u2026,n\uff09 \uff081.9\uff09
\u5176\u4e2d\uff0c \u662f\u5143\u7d20 \u5728D\u4e2d\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u3002
\u5b9a\u74061.2.1\uff08\u884c\u5217\u5f0f\u5c55\u5f00\u5b9a\u7406\uff09n\u9636\u884c\u5217\u5f0f \u7b49\u4e8e\u5b83\u7684\u4efb\u610f\u4e00\u884c\uff08\u5217\uff09\u7684\u5404\u5143\u7d20\u4e0e\u5176\u5bf9\u5e94\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u7684\u4e58\u79ef\u4e4b\u548c\uff0c\u5373
\uff08i=1,2,\u2026,n\uff09 \uff081.8\uff09
\u6216 \uff08j=1,2,\u2026,n\uff09 \uff081.9\uff09
\u5176\u4e2d\uff0c \u662f\u5143\u7d20 \u5728D\u4e2d\u7684\u4ee3\u6570\u4f59\u5b50\u5f0f\u3002
\uff081.8\uff09\u5f0f\u79f0\u4e3aD\u6309\u7b2ci\u884c\u7684\u5c55\u5f00\u5f0f\uff0c\uff081.9\uff09\u5f0f\u79f0\u4e3aD\u6309\u7b2cj\u5217\u7684\u5c55\u5f00\u5f0f\uff0c\u8fd9\u91cci,j=1,2,\u2026
\u4e0a\u8ff0\u5c55\u5f00\u5b9a\u7406\u4e5f\u53ef\u4ee5\u8868\u793a\u6210
\uff08i=1,2,\u2026,n\uff09
\uff08j=1,2,\u2026,n\uff09
\u8fd9\u4e24\u4e2a\u5c55\u5f00\u5f0f\u4e2d\u7684\u6bcf\u4e00\u9879\u90fd\u7531\u4e09\u90e8\u5206\u7ec4\u6210\uff1a\u5143\u7d20 \u548c\u5b83\u524d\u9762\u7684\u7b26\u53f7 \u4ee5\u53ca\u5b83\u540e\u9762\u7684\u4f59\u5b50\u5f0f \uff0c\u4e09\u8005\u7f3a\u4e00\u4e0d\u53ef\uff01\u7279\u522b\u5bb9\u6613\u5fd8\u6389\u7684\u662f\u628a\u5143\u7d20 \uff08\u7279\u522b\u662f \uff09\u6284\u5199\u4e0b\u6765\u3002
\u6839\u636e\u5b9a\u74061.2.1\u77e5\u9053\uff0c\u51e1\u662f\u542b\u96f6\u884c\uff08\u884c\u4e2d\u5143\u7d20\u5168\u4e3a\u96f6\uff09\u6216\u96f6\u5217\uff08\u5217\u4e2d\u5143\u7d20\u5168\u4e3a\u96f6\uff09\u7684\u884c\u5217\u5f0f\uff0c\u5176\u503c\u5fc5\u4e3a\u96f6\u3002
\u7279\u522b\u60c5\u5f62
\uff081\uff09
\uff082\uff09
\u4f8b5 \u8ba1\u7b97
[\u7b54\u7591\u7f16\u53f710010201\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u7531\u4e8e\u7b2c\u4e00\u884c\u6216\u7b2c\u56db\u5217\u6240\u542b\u96f6\u6700\u591a\uff0c\u6545\u53ef\u6309\u7b2c\u4e00\u884c\u5c55\u5f00
\u53ef\u89c1\u56db\u9636\u4e0b\u4e09\u89d2\u5f62\u884c\u5217\u5f0f\u7684\u503c\u4e5f\u7b49\u4e8e\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u5404\u6570\u4e4b\u79ef
\u4f8b5\u7684\u7ed3\u679c\u53ef\u63a8\u5e7f\u4e3a
\u6211\u4eec\u79f0\u8fd9\u79cd\u884c\u5217\u5f0f\u4e3a\u4e0b\u4e09\u89d2\u884c\u5217\u5f0f\uff08\u53ef\u4efb\u610f\u53d6\u503c\u7684\u5143\u7d20\u5728\u4e3b\u5bf9\u89d2\u7ebf\u7684\u4e0b\u9762\uff09\u3002
\u4f8b6 \u8ba1\u7b97
[\u7b54\u7591\u7f16\u53f710010202\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u7531\u4e8e\u7b2c2\u884c\u542b0\u6700\u591a\uff0c\u6240\u4ee5\u5e94\u6309\u7b2c\u4e8c\u884c\u5c55\u5f00
\u4f8b7 \u8ba1\u7b97
[\u7b54\u7591\u7f16\u53f710010203\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u5c06 \u6309\u7b2c6\u884c\u5c55\u5f00\u5f97
\u4f8b8 \u8ba1\u7b97
\uff081\uff09
[\u7b54\u7591\u7f16\u53f710010204\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u6309\u7b2c4\u884c\u5c55\u5f00
\uff082\uff09
[\u7b54\u7591\u7f16\u53f710010205\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u5c06D\u6309\u7b2c\u4e00\u884c\u5c55\u5f00
1.3 \u884c\u5217\u5f0f\u7684\u6027\u8d28\u4e0e\u8ba1\u7b97
\u56e0\u4e3an\u9636\u884c\u5217\u5f0f\u662fn!\u9879\u6c42\u548c\uff0c\u800c\u4e14\u6bcf\u4e00\u9879\u90fd\u662fn\u4e2a\u6570\u7684\u4e58\u79ef\uff0c\u5f53n\u6bd4\u8f83\u5927\u65f6\uff0c\u8ba1\u7b97\u91cf\u4f1a\u975e\u5e38\u5927\uff0c\u4f8b\u5982\uff0c10!=3628800\u3002\u6240\u4ee5\u5bf9\u4e8e\u9636\u6570\u8f83\u5927\u7684\u884c\u5217\u5f0f\u5f88\u96be\u76f4\u63a5\u7528\u5b9a\u4e49\u53bb\u6c42\u5b83\u7684\u503c\uff0c\u8fd9\u65f6\u5229\u7528\u884c\u5217\u5f0f\u7684\u6027\u8d28\u53ef\u4ee5\u6709\u6548\u5730\u89e3\u51b3\u884c\u5217\u5f0f\u7684\u6c42\u503c\u95ee\u9898\u3002\u4e0b\u9762\u6211\u4eec\u6765\u7814\u7a76\u884c\u5217\u5f0f\u7684\u6027\u8d28\uff0c\u5e76\u5229\u7528\u884c\u5217\u5f0f\u7684\u6027\u8d28\u6765\u7b80\u5316\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u3002
1.3.1 \u884c\u5217\u5f0f\u7684\u6027\u8d28
\u5c06\u884c\u5217\u5f0fD\u7684\u7b2c\u4e00\u884c\u6539\u4e3a\u7b2c\u4e00\u5217\uff0c\u7b2c\u4e8c\u884c\u6539\u4e3a\u7b2c\u4e8c\u5217\u2026\u2026\u7b2cn\u884c\u6539\u4e3a\u7b2cn\u5217\uff0c\u4ecd\u5f97\u5230\u4e00\u4e2an\u9636\u884c\u5217\u5f0f\uff0c\u8fd9\u4e2a\u65b0\u7684\u884c\u5217\u5f0f\u79f0\u4e3aD\u7684\u8f6c\u7f6e\u884c\u5217\u5f0f\uff0c\u8bb0\u4e3a \u6216 \u3002\u5373\u5982\u679c
\u5219
\u6027\u8d281 \u884c\u5217\u5f0f\u548c\u5b83\u7684\u8f6c\u7f6e\u884c\u5217\u5f0f\u76f8\u7b49\uff0c\u5373 \u6216
\u6839\u636e\u8fd9\u4e2a\u6027\u8d28\u53ef\u77e5\uff0c\u5728\u4efb\u610f\u4e00\u4e2a\u884c\u5217\u5f0f\u4e2d\uff0c\u884c\u4e0e\u5217\u662f\u5904\u4e8e\u5e73\u7b49\u5730\u4f4d\u7684\u3002\u51e1\u662f\u5bf9\u201c\u884c\u201d\u6210\u7acb\u7684\u6027\u8d28\uff0c\u5bf9\u201c\u5217\u201d\u4e5f\u6210\u7acb\uff1b\u53cd\u4e4b\uff0c\u51e1\u662f\u5bf9\u201c\u5217\u201d\u6210\u7acb\u7684\u6027\u8d28\uff0c\u5bf9\u201c\u884c\u201d\u4e5f\u6210\u7acb\u3002\u6240\u4ee5\u53ea\u9700\u7814\u7a76\u884c\u5217\u5f0f\u6709\u5173\u884c\u7684\u6027\u8d28\uff0c\u5176\u6240\u6709\u7ed3\u8bba\u5bf9\u5217\u4e5f\u662f\u81ea\u7136\u6210\u7acb\u7684\u3002
\u6027\u8d282 \u7528\u6570k\u4e58\u884c\u5217\u5f0fD\u4e2d\u67d0\u4e00\u884c\uff08\u5217\uff09\u7684\u6240\u6709\u5143\u7d20\u6240\u5f97\u5230\u7684\u884c\u5217\u5f0f\u7b49\u4e8ekD\u3002\u8fd9\u4e5f\u5c31\u662f\u8bf4\uff0c\u884c\u5217\u5f0f\u53ef\u4ee5\u6309\u884c\u548c\u6309\u5217\u63d0\u51fa\u516c\u56e0\u6570\uff1a
\u8bc1 \u5c06\u5de6\u8fb9\u7684\u884c\u5217\u5f0f \u6309\u5176\u7b2ci\u884c\u5c55\u5f00\u4ee5\u540e\uff0c\u518d\u63d0\u51fa\u516c\u56e0\u6570k\uff0c\u5373\u5f97\u53f3\u8fb9\u7684\u503c\uff1a
\u6ce8\u610f \u5982\u679c\u884c\u5217\u5f0f\u6709\u591a\u884c\u6216\u591a\u5217\u6709\u516c\u56e0\u6570\uff0c\u5fc5\u987b\u6309\u884c\u6216\u6309\u5217\u9010\u6b21\u63d0\u51fa\u516c\u56e0\u6570\u3002
\u4f8b1 \u8ba1\u7b97\u884c\u5217\u5f0f\uff1a
[\u7b54\u7591\u7f16\u53f710010206\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3
=30\uff084+6+5-2-4-15\uff09
=30\uff08-6\uff09=-180
\u5728\u4f8b1\u7684\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5148\u63d0\u51fa\u7b2c\u4e8c\u884c\u7684\u516c\u56e0\u65702\u548c\u7b2c\u4e09\u884c\u7684\u516c\u56e0\u65703\uff0c\u5f97\u5230\u7b2c\u4e00\u4e2a\u7b49\u53f7\u53f3\u8fb9\u7684\u5f0f\u5b50\uff0c\u7136\u540e\u63d0\u51fa\u8fd9\u4e2a\u884c\u5217\u5f0f\u4e2d\u7b2c\u4e09\u5217\u7684\u516c\u56e0\u65705\uff0c\u628a\u884c\u5217\u5f0f\u4e2d\u5404\u5143\u7d20\u7684\u7edd\u5bf9\u503c\u5316\u5c0f\u4ee5\u540e\uff0c\u518d\u6c42\u51fa\u539f\u884c\u5217\u5f0f\u7684\u503c\u3002
\u4f8b2
[\u7b54\u7591\u7f16\u53f710010207\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u56e0\u4e3a
\u6240\u4ee5\u539f\u5f0f=4abcdef
\u8fd9\u91cc\u662f\u628a\u4e0a\u5f0f\u7b2c\u4e00\u4e2a\u7b49\u53f7\u5de6\u8fb9\u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u3001\u4e8c\u3001\u4e09\u884c\u5206\u522b\u63d0\u51fa\u4e86\u516c\u56e0\u5b50a,d,f\uff0c\u7b2c\u4e8c\u4e2a\u7b49\u53f7\u5de6\u8fb9\u7684\u884c\u5217\u5f0f\u7684\u7b2c\u4e00\u3001\u4e8c\u3001\u4e09\u5217\u5206\u522b\u63d0\u51fa\u4e86\u516c\u56e0\u5b50b,c,e\uff0c\u5316\u7b80\u540e\u518d\u6c42\u51fa\u5176\u503c\u3002
\u4f8b3 \u8ba1\u7b97\u884c\u5217\u5f0f\uff1a
\u5728\u884c\u5217\u5f0fD\u7684\u6bcf\u4e00\u884c\u4e2d\u90fd\u63d0\u51fa\u516c\u56e0\u6570\uff08-1\uff09\u5e76\u7528\u884c\u5217\u5f0f\u6027\u8d281\u53ef\u4ee5\u5f97\u5230
[\u7b54\u7591\u7f16\u53f710010208\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u56e0\u4e3a\u884c\u5217\u5f0fD\u662f\u4e00\u4e2a\u6570\uff0c\u6240\u4ee5\u7531D= -D\uff0c\u53ef\u77e5\u884c\u5217\u5f0fD=0\u3002
\u7528\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u8bc1\u660e\uff1a\u4efb\u610f\u4e00\u4e2a\u5947\u6570\u9636\u53cd\u5bf9\u79f0\u884c\u5217\u5f0f\u5fc5\u4e3a\u96f6\u3002\u6240\u8c13\u53cd\u5bf9\u79f0\u884c\u5217\u5f0f\u6307\u7684\u662f\uff0c\u5176\u4e2d\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u4e3a0\uff0c\u800c\u4ee5\u4e3b\u5bf9\u89d2\u7ebf\u4e3a\u8f74\uff0c\u4e24\u8fb9\u5904\u4e8e\u5bf9\u79f0\u4f4d\u7f6e\u4e0a\u7684\u5143\u7d20\u5f02\u53f7\u3002\u5373\u82e5 \u662f\u53cd\u5bf9\u79f0\u884c\u5217\u5f0f\uff0c\u5219\u5b83\u6ee1\u8db3\u6761\u4ef6
\u6027\u8d283 \u4e92\u6362\u884c\u5217\u5f0f\u7684\u4efb\u610f\u4e24\u884c\uff08\u5217\uff09\uff0c\u884c\u5217\u5f0f\u7684\u503c\u6539\u53d8\u7b26\u53f7\u3002\u5373\u5bf9\u4e8e\u5982\u4e0b\u4e24\u4e2a\u884c\u5217\u5f0f
\u6709
\u6839\u636e\u8fd9\u4e2a\u6027\u8d28\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\u7684\u91cd\u8981\u63a8\u8bba\uff1a
\u63a8\u8bba \u5982\u679c\u884c\u5217\u5f0f\u4e2d\u6709\u4e24\u884c\uff08\u5217\uff09\u76f8\u540c\uff0c\u5219\u6b64\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u96f6\u3002
\u56e0\u4e3a\u4e92\u6362\u884c\u5217\u5f0fD\u4e2d\u7684\u4e24\u4e2a\u76f8\u540c\u7684\u884c\uff08\u5217\uff09\uff0c\u5176\u7ed3\u679c\u4ecd\u662fD\uff0c\u4f46\u7531\u6027\u8d283\u53ef\u77e5\u5176\u7ed3\u679c\u4e3a-D\uff0c\u56e0\u6b64D=-D\uff0c\u6240\u4ee5D=0\u3002
\u6027\u8d284 \u5982\u679c\u884c\u5217\u5f0f\u4e2d\u67d0\u4e24\u884c\uff08\u5217\uff09\u7684\u5bf9\u5e94\u5143\u7d20\u6210\u6bd4\u4f8b\uff0c\u5219\u6b64\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u96f6\u3002
\u8bc1 \u8bbe\u884c\u5217\u5f0fD\u7684\u7b2ci\u884c\u4e0e\u7b2cj\u884c\u7684\u5bf9\u5e94\u5143\u7d20\u6210\u6bd4\u4f8b\uff0c\u4e0d\u59a8\u8bbe\u7b2cj\u884c\u5143\u7d20\u662f\u7b2ci\u884c\u5143\u7d20\u4e58\u4ee5k\u5f97\u5230\u7684\uff0c\u5219
\u7531\u4e8e\u5c06\u884c\u5217\u5f0fD\u4e2d\u7b2cj\u884c\u7684\u6bd4\u4f8b\u7cfb\u6570k\u63d0\u5230\u884c\u5217\u5f0f\u7684\u5916\u9762\u6765\u4ee5\u540e\uff0c\u4f59\u4e0b\u7684\u884c\u5217\u5f0f\u6709\u4e24\u884c\u5bf9\u5e94\u5143\u7d20\u76f8\u540c\uff0c\u56e0\u6b64\u8be5\u884c\u5217\u5f0f\u7684\u503c\u4e3a\u96f6\uff0c\u4ece\u800c\u539f\u884c\u5217\u5f0f\u7684\u503c\u7b49\u4e8e\u96f6\u3002\u884c\u5217\u5f0f\u4e2d\u67d0\u4e24\u5217\u5143\u7d20\u5bf9\u5e94\u6210\u6bd4\u4f8b\u7684\u60c5\u5f62\u53ef\u4ee5\u7c7b\u4f3c\u5730\u8bc1\u660e\u3002
\u4f8b4 \u9a8c\u7b97x=3\u662f\u5426\u662f\u65b9\u7a0b \u7684\u6839\u3002
[\u7b54\u7591\u7f16\u53f710010209\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u89e3\uff1a\u56e0\u4e3a
\u2234x=3\u662f\u65b9\u7a0bf(x)=0\u7684\u6839\u3002
\u6027\u8d285 \u884c\u5217\u5f0f\u53ef\u4ee5\u6309\u884c\uff08\u5217\uff09\u62c6\u5f00\uff0c\u5373
\u8bc1 \u5c06\u5de6\u8fb9\u7684\u884c\u5217\u5f0f\u6309\u5176\u7b2ci\u884c\u5c55\u5f00\u5373\u5f97
\u8fd9\u5c31\u662f\u53f3\u8fb9\u4e24\u4e2a\u884c\u5217\u5f0f\u4e4b\u548c\u3002
\u6027\u8d286 \u628a\u884c\u5217\u5f0fD\u7684\u67d0\u4e00\u884c\uff08\u5217\uff09\u7684\u6240\u6709\u5143\u7d20\u90fd\u4e58\u4ee5\u540c\u4e00\u6570k\u4ee5\u540e\u52a0\u5230\u53e6\u4e00\u884c\uff08\u5217\uff09\u7684\u5bf9\u5e94\u5143\u7d20\u4e0a\u53bb\uff0c\u6240\u5f97\u7684\u884c\u5217\u5f0f\u4ecd\u4e3aD\u3002
\u5373\uff1a
\u4f8b5 \u8bc1\u660e\uff1a
\u7684\u5145\u8981\u6761\u4ef6\u662fk=1\u6216k=\u00b12
[\u7b54\u7591\u7f16\u53f710010301\uff1a\u9488\u5bf9\u8be5\u9898\u63d0\u95ee]
\u8bc1 \u56e0\u4e3a
\u6240\u4ee5\uff0cD=0\u7684\u5145\u8981\u6761\u4ef6\u662fk=1\u6216k=\u00b12\u3002
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