Question

向量组a1=(1 3 2 0);a2=( 2 -1 1 2);a3=( 1 2 4 1); a4=( 2 1 0 3),求秩及一个最大无关组

Answer 1

(a1,a2,a3,a4)=
1 2 1 2
3 -1 2 1
2 1 4 0
0 2 1 3
r2-r1-r3,r3-2r1
1 2 3 2
0 -4 -1 -1
0 -3 2 -4
0 2 1 3
r2+r4,r3-2r4
1 2 3 2
0 -2 0 2
0 -7 0 -10
0 2 1 3
r4+r2,r2*(-1/2),r3+7r2
1 2 3 2
0 1 0 -1
0 0 0 -17
0 0 1 5
所以向量组的秩为4,极大无关组为其自身.