求矩阵的秩可以将两行或两列互换吗? 矩阵的两行或两列可以互换吗?如果可以的话、是否像行列式一样变...

\u6c42\u77e9\u9635\u7684\u79e9\u53ef\u4ee5\u4ea4\u6362\u4e24\u884c\u7684\u4f4d\u7f6e\u5417\uff1f

\u53ef\u4ee5\u7684\uff0c\u77e9\u9635\u7684\u7684\u79e9=\u884c\u79e9=\u5217\u79e9\uff0c\u4ea4\u6362\u67d0\u4e24\u884c\u6216\u8005\u67d0\u4e24\u5217\u662f\u521d\u7b49\u884c\u53d8\u6362\u6216\u8005\u521d\u7b49\u5217\u53d8\u6362\uff0c\u77e9\u9635\u7684\u79e9\u4e0d\u4f1a\u53d8\u3002\u671b\u91c7\u7eb3~~~

1\u3001\u77e9\u9635\u7684\u4e24\u884c\u6216\u4e24\u5217\u53ef\u4ee5\u4e92\u6362\uff1b\u4e0d\u9700\u8981\u50cf\u884c\u5217\u5f0f\u4e00\u6837\u53d8\u53f7\u3002
2\u3001\u7406\u89e3\uff1a
\u4e00\u822c\u77e9\u9635\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u53ef\u4ee5\u770b\u6210\u662f\u65b9\u7a0b\u7ec4\u7684\u7cfb\u6570\u7ec4\u6210\u7684\uff0c\u672c\u8d28\u4e0a\u6765\u8bf4\u8bf4\u5c31\u662f\u4e00\u884c\u4e00\u884c\u7684\u65b9\u7a0b\u7ec4\u6784\u6210\u4e86\u77e9\u9635\uff0c\u7531\u6b64\u53ef\u60f3\uff0c\u5728\u65b9\u7a0b\u7ec4\u4e2d\u4ea4\u6362\u65b9\u7a0b\u7684\u4f4d\u7f6e\u5e76\u4e0d\u5f71\u54cd\u65b9\u7a0b\u6700\u7ec8\u7684\u7b54\u6848\uff0c\u5e94\u7528\u4e8e\u77e9\u9635\u4e5f\u4e00\u81f4\uff0c\u6240\u4ee5\u4ea4\u6362\u884c\u5217\u4e0d\u5f71\u54cd\u77e9\u9635\u3002
\u6b64\u5916\uff0c\u77e9\u9635\u5e76\u4e0d\u662f\u503c\uff0c\u4e0d\u5b58\u5728\u53d8\u53f7\u7684\u95ee\u9898\u3002

\u6269\u5c55\u8d44\u6599\uff1a
1\u3001\u5728\u6570\u5b66\u4e2d\uff0c\u77e9\u9635\u662f\u4e00\u4e2a\u6309\u7167\u957f\u65b9\u9635\u5217\u6392\u5217\u7684\u590d\u6570\u6216\u5b9e\u6570\u96c6\u5408 \uff0c\u6700\u65e9\u6765\u81ea\u4e8e\u65b9\u7a0b\u7ec4\u7684\u7cfb\u6570\u53ca\u5e38\u6570\u6240\u6784\u6210\u7684\u65b9\u9635\u3002
2\u3001\u4ea4\u6362\u77e9\u9635\u7684\u4e24\u884c\u6216\u8005\u5217\uff08\u5bf9\u8c03i,j\uff0c\u4e24\u884c\u8bb0\u4e3ari\uff0crj\uff09\u662f\u77e9\u9635\u7684\u521d\u7b49\u53d8\u6362\u4e4b\u4e00\uff1b
3\u3001\u82e5\u77e9\u9635A\u7ecf\u8fc7\u6709\u9650\u6b21\u7684\u521d\u7b49\u884c\u53d8\u6362\u53d8\u4e3a\u77e9\u9635B\uff0c\u5219\u77e9\u9635A\u4e0e\u77e9\u9635B\u884c\u7b49\u4ef7\uff1b\u82e5\u77e9\u9635A\u7ecf\u8fc7\u6709\u9650\u6b21\u7684\u521d\u7b49\u5217\u53d8\u6362\u53d8\u4e3a\u77e9\u9635B\uff0c\u5219\u77e9\u9635A\u4e0e\u77e9\u9635B\u5217\u7b49\u4ef7\uff1b\u82e5\u77e9\u9635A\u7ecf\u8fc7\u6709\u9650\u6b21\u7684\u521d\u7b49\u53d8\u6362\u53d8\u4e3a\u77e9\u9635B\uff0c\u5219\u77e9\u9635A\u4e0e\u77e9\u9635B\u7b49\u4ef7\u3002\u6240\u4ee5\u884c\u53d8\u6362\u4e0d\u6539\u53d8\u77e9\u9635\u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u77e9\u9635
\u767e\u5ea6\u767e\u79d1\u2014\u2014\u77e9\u9635\u53d8\u6362

求矩阵秩时,任何的初等变换都是可以的。
包括换行,换列,乘以系数,一行加到某一行等等

求秩的时候可以,求方程获特征值得时就不能换列

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  • 扩展阅读:行列式任意两列互换 ... 矩阵两行一样怎么求秩 ... 矩阵的秩怎么求 ... 一张图看懂矩阵运算 ... 行列式两列互换规则 ... 行列式某两列互换 ... 矩阵任意两行两列互换 ... 矩阵能不能两列互换 ... 行列式行列互换是相邻交换 ...

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