若α1=(2,1,-2),α2=(0,3,1),α3=(0,0,k-2)是3维行向量空间R3的基,则常数k满足
\u82e5\u03b11=(2,1,-2),\u03b12=(0,3,1),\u03b13=(0,0,k-2)\u662f3\u7ef4\u884c\u5411\u91cf\u7a7a\u95f4R3\u7684\u57fa\uff0c\u5219\u5e38\u6570k\u6ee1\u8db3\u65e2\u7136\u662f\u57fa\uff0c\u90a3\u4e48\u884c\u5217\u5f0f D=|a1 a2 a3| \u4e0d\u7b49\u4e8e 0 \uff0c
\u8ba1\u7b97\u5f97 D=6(k-2) \uff0c
\u56e0\u6b64 k \u6ee1\u8db3\uff1ak \u2260 2 \u3002
n\u4e2an\u7ef4\u5411\u91cf\u6784\u6210R^n\u7684\u57fa\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\u5b83\u4eec\u6784\u6210\u7684\u884c\u5217\u5f0f\u4e0d\u7b49\u4e8e0.
\u884c\u5217\u5f0f
2 1 -2
0 3 1
0 0 k-2
= 6(k-2)
\u2260 0.
\u6240\u4ee5 k\u22602.
\u6545 (A) \u6b63\u786e.
基的话,三个向量线性无关。
只要三个向量组成的矩阵A满足|A|≠0即可
|A|=6(k-2)≠0
k≠2
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