(α1,α2,α3,α4) =
1 1 1 4
1 -1 3 -2
2 1 3 5
3 1 3 6
r2-r1,r3-2r1,r4-3r1
1 1 1 4
0 -2 2 -6
0 -1 1 -3
0 -2 0 -6
r2-2r3, r4-2r3
1 1 1 4
0 0 0 0
0 -1 1 -3
0 0 -2 0
r1+r2+r3, r3+(1/2)r4
1 0 0 1
0 0 0 0
0 -1 0 -3
0 0 -2 0
r3*(-1), r4*(-1/2)
1 0 0 1
0 0 0 0
0 1 0 3
0 0 1 0
所以有: (1)向量组的秩为3, 线性相关
(2) α1,α2,α3 是一个极大无关组
(3) α4 = α1+3α2+0α3
满意请采纳^_^