求下列向量组的一个极大无关组，并将其它向量用此极大无关组线性表示 求下列向量组的秩和一个最大无关组 并把其余向量用最大无关组线...
\u6c42\u4e0b\u5217\u5411\u91cf\u7ec4\u7684\u79e9\u548c\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u5e76\u628a\u5176\u4f59\u5411\u91cf\u7528\u8be5\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u7ebf\u6027\u8868\u793a\u3002\u6c42\u4e0b\u5217\u5411\u91cf\u7ec4\u7684\u79e9\u548c\u4e00\u4e2a\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u5e76\u628a\u5176\u4f59\u5411\u91cf\u7528\u8be5\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u7ebf\u6027\u8868\u793a\uff1a
\u5411\u91cf\u7ec4\u7684\u79e9\u4e3a3\uff0ca1\uff0ca2\uff0ca3\u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\u3002\u5411\u91cf\u7ec4\u7684\u79e9\u4e3a\u7ebf\u6027\u4ee3\u6570\u7684\u57fa\u672c\u6982\u5ff5\uff0c\u5b83\u8868\u793a\u7684\u662f\u4e00\u4e2a\u5411\u91cf\u7ec4\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u6240\u542b\u5411\u91cf\u7684\u4e2a\u6570\u3002\u7531\u5411\u91cf\u7ec4\u7684\u79e9\u53ef\u4ee5\u5f15\u51fa\u77e9\u9635\u7684\u79e9\u7684\u5b9a\u4e49\u3002\u8981\u5b9a\u4e49\u5411\u91cf\u7ec4\u7684\u79e9\uff0c\u9996\u5148\u8981\u5b9a\u4e49\u6781\u5927\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u7ec4\u3002
\u5728\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u4e5f\u80fd\u628a\u5411\u91cf\u4ee5\u6570\u5bf9\u5f62\u5f0f\u8868\u793a\uff0c\u4f8b\u5982Oxy\u5e73\u9762\u4e2d(2\uff0c3)\u662f\u4e00\u5411\u91cf\u3002 \u5728\u7269\u7406\u5b66\u548c\u5de5\u7a0b\u5b66\u4e2d\uff0c\u51e0\u4f55\u5411\u91cf\u66f4\u5e38\u88ab\u79f0\u4e3a\u77e2\u91cf\u3002\u8bb8\u591a\u7269\u7406\u91cf\u90fd\u662f\u77e2\u91cf\uff0c\u6bd4\u5982\u4e00\u4e2a\u7269\u4f53\u7684\u4f4d\u79fb\uff0c\u7403\u649e\u5411\u5899\u800c\u5bf9\u5176\u65bd\u52a0\u7684\u529b\u7b49\u7b49\u3002
\u6982\u5ff5\u5206\u6790
\u4e0e\u4e4b\u76f8\u5bf9\u7684\u662f\u6807\u91cf\uff0c\u5373\u53ea\u6709\u5927\u5c0f\u800c\u6ca1\u6709\u65b9\u5411\u7684\u91cf\u3002\u4e00\u4e9b\u4e0e\u5411\u91cf\u6709\u5173\u7684\u5b9a\u4e49\u4ea6\u4e0e\u7269\u7406\u6982\u5ff5\u6709\u5bc6\u5207\u7684\u8054\u7cfb\uff0c\u4f8b\u5982\u5411\u91cf\u52bf\u5bf9\u5e94\u4e8e\u7269\u7406\u4e2d\u7684\u52bf\u80fd\u3002
\u51e0\u4f55\u5411\u91cf\u7684\u6982\u5ff5\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u7ecf\u7531\u62bd\u8c61\u5316\uff0c\u5f97\u5230\u66f4\u4e00\u822c\u7684\u5411\u91cf\u6982\u5ff5\u3002\u6b64\u5904\u5411\u91cf\u5b9a\u4e49\u4e3a\u5411\u91cf\u7a7a\u95f4\u7684\u5143\u7d20\uff0c\u8981\u6ce8\u610f\u8fd9\u4e9b\u62bd\u8c61\u610f\u4e49\u4e0a\u7684\u5411\u91cf\u4e0d\u4e00\u5b9a\u4ee5\u6570\u5bf9\u8868\u793a\uff0c\u5927\u5c0f\u548c\u65b9\u5411\u7684\u6982\u5ff5\u4ea6\u4e0d\u4e00\u5b9a\u9002\u7528\u3002
1 7 2 5 2
3 0 -1 1 -1
2 14 0 6 4
0 3 1 2 1
\u7b2c2\u884c,\u7b2c3\u884c, \u52a0\u4e0a\u7b2c1\u884c\u00d7-3,-2
1 7 2 5 2
0 -21 -7 -14 -7
0 0 -4 -4 0
0 3 1 2 1
\u7b2c1\u884c,\u7b2c4\u884c, \u52a0\u4e0a\u7b2c2\u884c\u00d71/3,1/7
1 0 -1/3 1/3 -1/3
0 -21 -7 -14 -7
0 0 -4 -4 0
0 0 0 0 0
\u7b2c1\u884c,\u7b2c2\u884c, \u52a0\u4e0a\u7b2c3\u884c\u00d7-1/12,-7/4
1 0 0 2/3 -1/3
0 -21 0 -7 -7
0 0 -4 -4 0
0 0 0 0 0
\u7b2c2\u884c,\u7b2c3\u884c, \u63d0\u53d6\u516c\u56e0\u5b50-21,-4
1 0 0 2/3 -1/3
0 1 0 1/3 1/3
0 0 1 1 0
0 0 0 0 0
\u79e9\u7b49\u4e8e3
\u6700\u5927\u65e0\u5173\u7ec4\uff1aa1,a2,a3
a4\uff1d2a1/3+a2/3+a3
a5=-a1/3+a2/3
1 0 0 2
0 1 0 -1
1 0 1 3
1 -1 -3 0
r3-r1,r4-r1
1 0 0 2
0 1 0 -1
0 0 1 1
0 -1 -3 -2
r3+r2+3r3
1 0 0 2
0 1 0 -1
0 0 1 1
0 0 0 0
所以α1,α2,α3是一个极大无关组, α4=2α1-α2+α3.
满意请采纳^_^
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