求向量组a1a2a3a4a5的秩,判断相关性,求向量组a1a2a3a4a5一个极大无关组,并将其余向量由此极大无关组线性a1=(1123)a2=(1-111)a3=(1335)a4=(4-256)a5=(-3-1-5-7)

Question

求向量组a1a2a3a4a5的秩,判断相关性,求向量组a1a2a3a4a5一个极大无关组,并将其余向量由此极大无关组线性
a1=(1123)a2=(1-111)a3=(1335)a4=(4-256)a5=(-3-1-5-7)

Answer 1

(a1,a2,a3,a4,a5)=
1 1 1 4 -3
1 -1 3 -2 -1
2 1 3 5 -5
3 1 5 6 -7
r4-r3
1 1 1 4 -3
1 -1 3 -2 -1
2 1 3 5 -5
1 0 2 1 -2
r1-r4,r2-r4,r3-2r4
0 1 -1 3 -1
0 -1 1 -3 1
0 1 -1 3 -1
1 0 2 1 -2
r2+r1,r3-r1
0 1 -1 3 -1
0 0 0 0 0
0 0 0 0 0
1 0 2 1 -2
交换行得
1 0 2 1 -2
0 1 -1 3 -1
0 0 0 0 0
0 0 0 0 0
(1) a1,a2 是一个极大无关组
(2) a3=2a1-a2,a4=a1+3a2,a5=-2a1-a2