【线代题】求一个向量的极大无关组,并用其余向量用此极大无关组表示. 求下列向量组的一个极大无关组，并将其余向量用此极大无关组线性...
\u6c42\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\uff0c\u5e76\u7528\u6b64\u6781\u5927\u65e0\u5173\u7ec4\u8868\u793a\u5176\u4f59\u5411\u91cf\u5bf9\u5411\u91cf\u7ec4\u505a\u521d\u7b49\u5217\u53d8\u6362\u3002
\u9009\u53d6\u03b11\uff0c\u03b12\uff0c\u03b13\u4e3a\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4\u3002
\u03b14 = \u03b11+\u03b13
\u6ce8\u610f\uff1a
\u5bf9\u4e8e\u884c\u5411\u91cf\u505a\u521d\u7b49\u5217\u53d8\u6362\u4e0d\u6539\u53d8\u5176\u7ebf\u6027\u76f8\u5173\u6027\u3002
\u5bf9\u4e8e\u5217\u5411\u91cf\u505a\u521d\u7b49\u884c\u53d8\u6362\u4e0d\u6539\u53d8\u7ebf\u6027\u76f8\u5173\u6027\u3002
\u6b64\u9898\u53ef\u4ee5\u5c06\u5411\u91cf\u5199\u6210\u5217\u5411\u91cf\uff0c\u518d\u505a\u884c\u53d8\u6362\u3002
newmanhero 2015\u5e746\u67085\u65e523:59:56
\u5e0c\u671b\u5bf9\u4f60\u6709\u6240\u5e2e\u52a9\uff0c\u671b\u91c7\u7eb3\u3002
\u89e3: (a1^T,a2^T,a3^T,a4^T) =
2 -1 3 8
1 1 1 5
1 7 -1 9
1 10 -2 11
r1-2r2,r3-r2,r4-r2
0 -3 1 -2
1 1 1 5
0 6 -2 4
0 9 -3 6
r3+2r1,r4+3r1,r2-r1
0 -3 1 -2
1 4 0 7
0 0 0 0
0 0 0 0
\u6240\u4ee5 a1,a3 \u662f\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4
a2 = 4a1 - 3a3a4 = 7a1 - 2a3
1 -1 5 -1
1 1 -2 3
3 -1 8 1
1 3 -9 7
r2-r1,r3-3r1,r4-r1
1 -1 5 -1
0 2 -7 4
0 2 -7 4
0 4 -14 8
r3-r2,r4-2r2, r2*(1/2),r2+r1
1 0 3/2 1
0 1 -7/2 2
0 0 0 0
0 0 0 0
α1,α2 是一个极大无关组
α3 = 3/2α1 - 7/2α2
α4 = α1 + 2α2
极大无关组：a1,a2；a3=(3a1-7a2)/2，a4=a1+2a2
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