Question

已知向量组M：a1=(1 -2 2 3),a2=(-2 4 -1 3),a3=(-1 2 0 3),a4=(2 -6 3

Answer 1

(a1,a2,a3,a4)=

1 -2 -1 2

-2 4 2 -6

2 -1 0 3

3 3 3 4

r2+2r1,r3-2r1,r4-3r1

1 -2 -1 2

0 0 0 -2

0 3 2 -1

0 9 6 -2

r2*(-1/2),r1-2r2,r3+r2,r4+2r2

1 -2 -1 0

0 0 0 1

0 3 2 0

0 9 6 0

r4-3r3,r3*(1/3),r1+2r3

1 0 1/3 0

0 0 0 1

0 1 2/3 0

0 0 0 0

向量组的秩为3,向量组线性相关

a1,a2,a4 是M的一个极大无关组,且 a3=(1/3)a1+(2/3)a2.