向量a1 a2 a3 a4为三维非零列向量 线性代数向量模块问题 设a1 a2 a3 a4 是三维列向量...

\u5df2\u77e5a1\uff0ca2\uff0ca3\uff0ca4\u662f\u56db\u7ef4\u975e0\u5217\u5411\u91cf\uff0c \u8bb0A=\uff08a1\uff0ca2\uff0ca3\uff0ca4\uff09\uff0cA*\u662fA\u7684\u4f34\u968f\u77e9\u9635

D\u3001a2\uff0ca3\uff0ca4\u3002
\u5177\u4f53\u8fc7\u7a0b\u5982\u56fe\uff1a



\u4e00\u822c\u7ed3\u8bba\u662fA\uff0c\u4f46B\u4e2d\u5411\u91cf\u4e5f\u662fa1\uff0ca2\uff0ca3\u7684\u4e00\u4e2a\u7b49\u4ef7\u5411\u91cf\u7ec4\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u4e3b\u5bf9\u89d2\u5143\u7d20\u662f\u5c06\u539f\u77e9\u9635\u8be5\u5143\u7d20\u6240\u5728\u884c\u5217\u53bb\u6389\u518d\u6c42\u884c\u5217\u5f0f\uff0c\u975e\u4e3b\u5bf9\u89d2\u5143\u7d20\u662f\u539f\u77e9\u9635\u8be5\u5143\u7d20\u7684\u5171\u8f6d\u4f4d\u7f6e\u7684\u5143\u7d20\u53bb\u6389\u6240\u5728\u884c\u5217\u6c42\u884c\u5217\u5f0f\u3002
\u5f53\u77e9\u9635\u7684\u9636\u6570\u7b49\u4e8e\u4e00\u9636\u65f6\uff0c\u4f34\u968f\u77e9\u9635\u4e3a\u4e00\u9636\u5355\u4f4d\u65b9\u9635\u3002\u4e8c\u9636\u77e9\u9635\u7684\u6c42\u6cd5\u53e3\u8bc0\uff1a\u4e3b\u5bf9\u89d2\u7ebf\u5143\u7d20\u4e92\u6362\uff0c\u526f\u5bf9\u89d2\u7ebf\u5143\u7d20\u53d8\u53f7\u3002

\u56e0\u4e3aa1 a2 a3 a4 \u662f\u4e09\u7ef4\u5217\u5411\u91cf
\u6240\u4ee5r\uff08a1,a2,a3,a4\uff09\u22643
\u5047\u8bbe\u5168\u90e8\u4e3a\u975e\u96f6\u5411\u91cf\uff0c\u7531\u4e24\u4e24\u6b63\u4ea4\u53ef\u5f97
a1 a2 a3 a4\u7ebf\u6027\u65e0\u5173
\u6240\u4ee5r(a1,a2,a3,a4)=4,\u77db\u76fe
\u6240\u4ee5\u81f3\u5c11\u4e00\u4e2a\u96f6\u5411\u91cf

A = (a1, a2, a3, a4) 是 3×4 矩阵，
a1, a2, a3 线性无关， 则 r(A) = 3, 即 r(a1, a2, a3, a4) = 3.
4个向量， r(a1, a2, a3, a4) = 3 < 4 , 故线性相关，
a1, a2, a3 向量组的极大无关租，a4 可由a1, a2, a3 线性表出。

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