四行三列矩阵的秩 矩阵的秩怎么求五行四列
3\u884c4\u5217\u77e9\u9635\u7684\u79e9\u600e\u4e48\u6c42\u554a\uff1f\u7ed9\u4e2a\u4f8b\u9898\u89e3\u7b54\u8c22\u8c22\u4e86\u505a\u884c\u521d\u7b49\u53d8\u6362\uff0c\u628a\u77e9\u9635\u6362\u6210\u6807\u51c6\u578b\uff0c\u6709\u51e0\u884c\u4e0d\u5168\u4e3a0\u7684\u884c\uff0c\u79e9\u5c31\u662f\u51e0\u3002
\u4f8b\u5982\uff1a
1 1 1 2
1 2 1 3
1 3 2 5
\u7b2c1\u884c\u7684-1\u500d\u52a0\u5230\u7b2c2\u30013\u884c\uff1a
1 1 1 2
0 1 0 1
0 2 1 3
\u7b2c2\u884c\u7684-1\u500d\u52a0\u5230\u7b2c1\u884c\uff0c\u7b2c2\u884c\u7684-2\u500d\u52a0\u5230\u7b2c3\u884c\uff1a
1 0 1 1
0 1 0 1
0 0 0 1
\u7b2c3\u884c\u7684-1\u500d\u52a0\u5230\u7b2c1\u30012\u884c\uff1a
1 0 1 0
0 1 0 0
0 0 0 1
\u4e0d\u5168\u4e3a0\u7684\u884c\u67093\u884c\uff0c\u539f\u67653\u884c4\u5217\u77e9\u9635\u7684\u79e9\u662f3.
\u7c7b\u4f3c\u5730\uff0c3\u884c4\u5217\u77e9\u9635
1 1 1 2
1 2 1 3
1 3 1 4
\u7ecf\u8fc7\u884c\u521d\u7b49\u53d8\u6362\u540e\uff0c\u53ef\u5f97\u8fd9\u4e2a3\u884c4\u5217\u77e9\u9635\u7684\u79e9\u662f2\u3002
\u4e00\u4e2ax\u884cy\u5217\u7684\u77e9\u9635\u7ef4\u6570\u662f\u591a\u5c11?\u8fd9\u8981\u770b\u5177\u4f53\u60c5\u51b5\u7684.\u77e9\u9635\u7684\u7ef4\u6570\u5c31\u662f\u901a\u5e38\u6240\u8bf4\u7684\u79e9.
\u5b9a\u7406: \u4e00\u4e2a\u77e9\u9635\u7684\u884c\u7a7a\u95f4\u7684\u7ef4\u6570\u7b49\u4e8e\u5217\u7a7a\u95f4\u7684\u7ef4\u6570,\u7b49\u4e8e\u8fd9\u4e2a\u77e9\u9635\u7684\u79e9.
\u5b9a\u4e49:
A=(aij)m\u00d7n\u7684\u4e0d\u4e3a\u96f6\u7684\u5b50\u5f0f\u7684\u6700\u5927\u9636\u6570\u79f0\u4e3a\u77e9\u9635A
\u7684\u79e9\uff0c\u8bb0\u4f5crA\uff0c\u6216rankA\u3002
\u7279\u522b\u89c4\u5b9a\u96f6\u77e9\u9635\u7684\u79e9\u4e3a\u96f6\u3002
\u663e\u7136rA\u2264min(m,n) \u6613\u5f97\uff1a
\u82e5A\u4e2d\u81f3\u5c11\u6709\u4e00\u4e2ar\u9636\u5b50\u5f0f\u4e0d\u7b49\u4e8e\u96f6\uff0c\u4e14\u5728r<min(m,n)\u65f6\uff0cA\u4e2d\u6240\u6709\u7684r+1\u9636\u5b50\u5f0f\u5168\u4e3a\u96f6\uff0c\u5219A\u7684\u79e9\u4e3ar\u3002
\u4e5f\u5c31\u662f\u8981\u8ba1\u7b97\u5b83\u7684\u5b50\u5f0f,\u5f53\u8ba1\u7b97\u81f3r\u9636\u5b50\u5f0f\u4e0d\u7b49\u4e8e\u96f6,\u800cr+1\u9636\u5b50\u5f0f\u7b49\u4e8e\u96f6\u65f6,\u77e9\u9635\u7684\u7ef4\u6570(\u79e9)\u5c31\u4e3ar
假设为
a1 a2 a3
b1 b2 b3
c1 c2 c3
d1 d2 d3
其中a-c行线性无关，则向量a,b,c为基底，一定可以表示出d=xa+yb+zc
根据矩阵的秩的概念，矩阵的秩一定小于或等于它的行数和列数中小的那个数，所以四行三列的矩阵，它的秩一定小于或等于3。
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