Question

求向量组a1=(-1,2,2)^T,a2=(2,-1,2)^T,a3=(2,2,-1)^T,a4=(1,7,-2)^T的

Answer 1

(a1,a2,a3,a4) =

-1 2 2 1

2 -1 2 7

2 2 -1 -2

r2+2r1,r3+2r1

-1 2 2 1

0 3 6 9

0 6 3 0

r1*(-1),r3-2r2,r2*(1/3)

1 -2 -2 -1

0 1 2 3

0 0 -9 -18

r3*(-1/9),r1+2r3,r2-2r3

1 -2 0 3

0 1 0 -1

0 0 1 2

r1+2r2

1 0 0 1

0 1 0 -1

0 0 1 2

向量组的秩为3,a1,a2,a3 是一个极大无关组.

a4 = a1-a2+2a3.