求下列向量组的秩和一个最大无关组,a1=(1,2,1,3)a2=(4,-1,-5,-6)a3=(-1,-3,-4,-7）a4=(2,1,2,3),求过程?

Question

求下列向量组的秩和一个最大无关组,a1=(1,2,1,3)a2=(4,-1,-5,-6)a3=(-1,-3,-4,-7）a4=(2,1,2,3),求过程?

Answer 1

(a1^T,a2^T,a3^T,a4^T)=
1 4 -1 2
2 -1 -3 1
1 -5 -4 2
3 -6 -7 3
r4-r2-r3,r2-2r1,r3-r1
1 4 -1 2
0 -9 -1 -3
0 -9 -3 0
0 0 0 0
r3-r2
1 4 -1 2
0 -9 -1 -3
0 0 -2 3
0 0 0 0
向量组的秩为3, a1,a2,a3是一个极大无关组.