设向量组α1=(1,0,0,0),α2=(0,1,0,0),α3=(0,0,1,0),α4=(0,

0,0,1),则它的最大线性无关组是?
2025-02-27 01:53:39
推荐回答(1个)
回答1:

参考啦
解: (a1,a2,a3,a4)=
1 2 1 3
-1 1 -1 0
0 5 -2 7
4 6 0 14

r2+r1,r4-4r1
1 2 1 3
0 3 0 3
0 5 -2 7
0 -2 -4 2

r2*(1/3), r1-2r2,r3-5r2,r4+2r2
1 0 1 1
0 1 0 1
0 0 -2 2
0 0 -4 4

r3*(-1/2),r1-r3,r4+4r3
1 0 0 2
0 1 0 1
0 0 1 -1
0 0 0 0

所, a1,a2,a3 极关组
a4=2a1+a2-a3.
好评,谢谢啦