Question

设向量组A:a1=(1,4,1,0),a2=(2,1,-1,3),a3=(1,0,-3,-1),a4=(0,3,-1,-4),求向量组的秩及一个极大线性无关组

Answer 1

(a1,a2,a3,a4)=
1 2 1 0
4 1 0 3
1 -1 -3 -1
0 3 -1 -4

r1-r3,r2-4r3
0 3 4 1
0 5 12 7
1 -1 -3 -1
0 3 -1 -4

r2-2r1,r3-r1
0 3 4 1
0 -1 4 5
1 -1 -3 -1
0 0 -5 -5

r1+3r2
0 0 16 16
0 -1 4 5
1 -1 -3 -1
0 0 -5 -5

r1*(1/16),r4+5r1
0 0 1 1
0 -1 4 5
1 -1 -3 -1
0 0 0 0

向量组的秩为3, a1,a2,a3 是一个极大无关组.