Question

已知a1=(1,4,1,0),a2=(2,9,-1,-3),a3=(1,0,-3,-1),a4=(3,10,-7,-7)

Answer 1

(a1,a2,a3,a4)=

1 2 1 3

4 9 0 10

1 -1 -3 -7

0 -3 -1 -7

r2-4r1,r3-r1

1 2 1 3

0 1 -4 -2

0 -3 -4 -10

0 -3 -1 -7

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

1 0 9 7

0 1 -4 -2

0 0 -16 -16

0 0 3 3

r4*(1/3),r1-9r4,r2+4r4,r3+16r4

1 0 0 -2

0 1 0 2

0 0 0 0

0 0 1 1

所以向量组的秩为 3

a1,a2,a3 是一个极大无关组

且 a4 = -2a1+2a2+a3