任意三维非0列向量都能由三个线性无关的向量来表示吗？ 一组线性无关的向量可以表示任意同维向量吗
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1\u3001\u4ece\u5411\u91cf\u7ec4\u4e0e\u5b83\u90e8\u5206\u7ec4\u7684\u5173\u7cfb\u6765\u770b\uff1a
\u82e5\u5411\u91cf\u7ec4\u7684\u4e00\u4e2a\u90e8\u5206\u7ec4\u7ebf\u6027\u76f8\u5173
⇔\uff3cLeftrightarrow⇔\u5219\u6574\u4e2a\u5411\u91cf\u7ec4\u7ebf\u6027\u76f8\u5173\uff0e
\u82e5\u5411\u91cf\u7ec4\u7ebf\u6027\u65e0\u5173
⇔\uff3cLeftrightarrow⇔\u5219\u5b83\u7684\u4efb\u4f55\u4e00\u4e2a\u90e8\u5206\u5411\u91cf\u7ec4\u7ebf\u6027\u65e0\u5173\uff0e
\uff08\u4ee5\u4e0a\u4e8c\u8005\u4e3a\u9006\u5426\u547d\u9898\uff09
2\u3001\u4ece\u5411\u91cf\u7ec4\u4e0e\u5b83\u7684\u5ef6\u4f38\u7ec4\u6216\u4f38\u7f29\u7ec4\u7684\u5173\u7cfb\u6765\u770b\uff1a
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\u6269\u5c55\u8d44\u6599
\u4e3e\u4f8b\uff1a
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\u6240\u4ee5\u79e9\uff08\u5411\u91cf\u7ec4a1\uff0ca2\uff0ca3\uff0ca4\uff09\uff1d4
\u53c8\u56e0\u4e3a\u79e9\uff08\u5411\u91cf\u7ec4b1\uff0cb2\uff0cb3\uff0cb4\uff09\u3002
换成任意指定的3个线性无关的向量α1，α2，α3也行。由于任意4个3维向量一定线性相关，即α1，α2，α3，β线性相关，根据定理，β一定可由α1，α2，α3线性表示，且表示方法唯一。
对的，而且就算不是非零也是可以的
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