交换矩阵的两行或两列有什么情况 矩阵能直接进行两列互换吗?

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2\u3001\u7406\u89e3\uff1a
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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
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\u77e9\u9635\u7b49\u4ef7\u6027\u8d28\uff1a
1\u3001\u53cd\u8eab\u6027 A~A\uff1b
2\u3001\u5bf9\u79f0\u6027 \u82e5A~B\uff0c\u5219B~A\uff1b
3\u3001\u4f20\u9012\u6027 \u82e5A~B\uff0cB~C\uff0c\u5219A~C\u3002

首先矩阵的两行或两列是可以进行交换的,与它行列式不同,行列式变换行和列的时候需要进行符号的改变。而矩阵的变化则是等价的,不会产生什么影响,特别是在线性代数中我们会对矩阵求秩,在这个过程中两行或两列交换是没有影响的,但是有的时候,我们通常会把矩阵和方程组联系在一起,从而来求方程组的解,在这个过程中我们会对其进行初等变换,但如果列变换就会使自变量系数交换从导致方程解的改变,因此在用矩阵求解方程组的时候只能够进行行变换,大家就要注意了

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