线性代数求下列向量组的秩及其一个极大无关组,将其余向量组用极大无关组线性表出6 1 1 74 0 4 1A1= 1 A2

(a1,a2,a3,a4) =
6 1 1 7
4 0 4 1
1 2 -9 0
-1 3 -16 -1
2 -4 22 3
r1-6r3,r2-4r3,r4+r3,r5-2r3
0 -11 55 7
0 -8 40 1
1 2 -9 0
0 5 -25 -1
0 -8 40 3
r1+2r4, r5-r2,
0 -1 5 5
0 -8 40 1
1 2 -9 0
0 5 -25 -1
0 0 0 2
r5*(1/2), r1-5r5,r2-r5,r4+r5
0 -1 5 0
0 -8 40 0
1 2 -9 0
0 5 -25 0
0 0 0 1
r2-8r1, r3+2r1, r4+5r1
0 -1 5 0
0 0 0 0
1 0 1 0
0 0 0 0
0 0 0 1
r1*(-1), 交换行得
1 0 1 0
0 1 -5 0
0 0 0 1
0 0 0 0
0 0 0 0
向量组的秩 = 3, a1,a2,a4 是向量组的一个极大无关组, 且
a3 = a1-5a2+0a4.
满意请采纳^_^.