同学们,求矩阵的秩可以行列变换混用吗 矩阵的初等变换行列可以一起用吗

\u6c42\u77e9\u9635\u79e9\u7684\u65f6\u5019\uff0c\u53ef\u4ee5\u4ea4\u66ff\u4f7f\u7528\u884c\u5217\u53d8\u6362\u5417

\u5982\u679c\u53ea\u662f\u6c42\u79e9\uff0c\u53ef\u4ee5\u4efb\u610f\u4f7f\u7528\u884c\u5217\u53d8\u6362\u3002\u4f46\u5982\u679c\u8fd8\u8981\u6c42\u5217\u5411\u91cf\u7ec4\u7684\u6781\u5927\u65e0\u5173\u7ec4\u7b49\uff0c\u5219\u53ea\u80fd\u7528\u884c\u53d8\u6362\u3002
\u4e00\u4e2a\u77e9\u9635A\u7684\u5217\u79e9\u662fA\u7684\u7ebf\u6027\u72ec\u7acb\u7684\u7eb5\u5217\u7684\u6781\u5927\u6570\u76ee\u3002\u7c7b\u4f3c\u5730\uff0c\u884c\u79e9\u662fA\u7684\u7ebf\u6027\u65e0\u5173\u7684\u6a2a\u884c\u7684\u6781\u5927\u6570\u76ee\u3002\u901a\u4fd7\u4e00\u70b9\u8bf4\uff0c\u5982\u679c\u628a\u77e9\u9635\u770b\u6210\u4e00\u4e2a\u4e2a\u884c\u5411\u91cf\u6216\u8005\u5217\u5411\u91cf\uff0c\u79e9\u5c31\u662f\u8fd9\u4e9b\u884c\u5411\u91cf\u6216\u8005\u5217\u5411\u91cf\u7684\u79e9\uff0c\u4e5f\u5c31\u662f\u6781\u5927\u65e0\u5173\u7ec4\u4e2d\u6240\u542b\u5411\u91cf\u7684\u4e2a\u6570\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u5728m*n\u77e9\u9635A\u4e2d\uff0c\u4efb\u610f\u51b3\u5b9ak\u884c\u548ck\u5217\u4ea4\u53c9\u70b9\u4e0a\u7684\u5143\u7d20\u6784\u6210A\u7684\u4e00\u4e2ak\u9636\u5b50\u77e9\u9635\uff0c\u6b64\u5b50\u77e9\u9635\u7684\u884c\u5217\u5f0f\uff0c\u79f0\u4e3aA\u7684\u4e00\u4e2ak\u9636\u5b50\u5f0f\u3002
\u4f8b\u5982\uff0c\u5728\u9636\u68af\u5f62\u77e9\u9635\u4e2d\uff0c\u9009\u5b9a1\uff0c3\u884c\u548c3\uff0c4\u5217\uff0c\u5b83\u4eec\u4ea4\u53c9\u70b9\u4e0a\u7684\u5143\u7d20\u6240\u7ec4\u6210\u76842\u9636\u5b50\u77e9\u9635\u7684\u884c\u5217\u5f0f \u5c31\u662f\u77e9\u9635A\u7684\u4e00\u4e2a2\u9636\u5b50\u5f0f\u3002
\u5f53r(A)<=n-2\u65f6\uff0c\u6700\u9ad8\u9636\u975e\u96f6\u5b50\u5f0f\u7684\u9636\u6570<=n-2\uff0c\u4efb\u4f55n-1\u9636\u5b50\u5f0f\u5747\u4e3a\u96f6\uff0c\u800c\u4f34\u968f\u9635\u4e2d\u7684\u5404\u5143\u7d20\u5c31\u662fn-1\u9636\u5b50\u5f0f\u518d\u52a0\u4e0a\u4e2a\u6b63\u8d1f\u53f7\uff0c\u6240\u4ee5\u4f34\u968f\u9635\u4e3a0\u77e9\u9635\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u77e9\u9635\u7684\u79e9

\u884c\u5217\u53d8\u6362\u7684\u7528\u6cd5\u8981\u770b\u5177\u4f53\u60c5\u51b5\u3002
\u6c42\u884c\u6700\u7b80\u5f62\uff0c\u9636\u68af\u77e9\u9635\uff0c\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u6781\u5927\u65e0\u5173\u7ec4\u65f6\u53ea\u80fd\u7528\u884c\u53d8\u6362\uff0c\u56e0\u4e3a\u6b64\u65f6\u7684\u5217\u53d8\u6362\u4f1a\u6253\u4e71\u672a\u77e5\u91cf\u7684\u987a\u5e8f\u6c42\u7b49\u4ef7\u6807\u51c6\u5f62\uff0c\u77e9\u9635\u7684\u79e9\u53ef\u884c\u5217\u53d8\u6362\u6df7\u7528\uff0c\u521d\u7b49\u53d8\u6362\u77e9\u9635\u7684\u79e9\u4e0d\u53d8\uff0c\u4ecd\u4e0e\u539f\u77e9\u9635\u7b49\u4ef7\u3002
\u521d\u7b49\u53d8\u6362\uff08elementary transformation\uff09\u662f\u4e09\u79cd\u57fa\u672c\u7684\u53d8\u6362\uff0c\u51fa\u73b0\u5728\u300a\u9ad8\u7b49\u4ee3\u6570\u300b\u4e2d\u3002\u521d\u7b49\u53d8\u6362\u5305\u62ec\uff1a\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u521d\u7b49\u53d8\u6362\u3001\u884c\u5217\u5f0f\u7684\u521d\u7b49\u53d8\u6362\u548c\u77e9\u9635\u7684\u521d\u7b49\u53d8\u6362\uff0c\u8fd9\u4e09\u8005\u5728\u672c\u8d28\u4e0a\u662f\u4e00\u6837\u7684\u3002
\u521d\u7b49\u884c\u53d8\u6362
\u5b9a\u4e49\uff1a\u6240\u8c13\u6570\u57dfP\u4e0a\u77e9\u9635\u7684\u521d\u7b49\u884c\u53d8\u6362\u662f\u6307\u4e0b\u52173\u79cd\u53d8\u6362\uff1a
1\uff09\u4ee5P\u4e2d\u4e00\u4e2a\u975e\u96f6\u7684\u6570\u4e58\u77e9\u9635\u7684\u67d0\u4e00\u884c
2\uff09\u628a\u77e9\u9635\u7684\u67d0\u4e00\u884c\u7684c\u500d\u52a0\u5230\u53e6\u4e00\u884c\uff0c\u8fd9\u91ccc\u662fP\u4e2d\u7684\u4efb\u610f\u4e00\u4e2a\u6570
3\uff09\u4e92\u6362\u77e9\u9635\u4e2d\u4e24\u884c\u7684\u4f4d\u7f6e
\u4e00\u822c\u6765\u8bf4\uff0c\u4e00\u4e2a\u77e9\u9635\u7ecf\u8fc7\u521d\u7b49\u884c\u53d8\u6362\u540e\u5c31\u53d8\u6210\u4e86\u53e6\u4e00\u4e2a\u77e9\u9635\uff0c\u5f53\u77e9\u9635A\u7ecf\u8fc7\u521d\u7b49\u884c\u53d8\u6362\u53d8\u6210\u77e9\u9635B\u65f6\uff0c\u4e00\u822c\u5199\u4f5c\u53ef\u4ee5\u8bc1\u660e\uff1a\u4efb\u610f\u4e00\u4e2a\u77e9\u9635\u7ecf\u8fc7\u4e00\u7cfb\u5217\u521d\u7b49\u884c\u53d8\u6362\u603b\u80fd\u53d8\u6210\u9636\u68af\u578b\u77e9\u9635\u3002

可以行列初等变换混用。

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  • 扩展阅读:什么时候不能行列混用 ... 矩阵为什么不能列变换 ... 求秩可以行列混用吗 ... 矩阵的秩可以列变换吗 ... 行列式可以行列混用吗 ... 矩阵不能用行列变换吗 ... 可以行列混用的情况 ... 矩阵的秩只能行变换吗 ... 矩阵可以行列一起变吗 ...

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