Question

用行初等变换求矩阵的逆矩阵：求x1=(1,2,2)的转置,X2=(2,-2,1)的转置,X3=(-2,-1,2)的转置

Answer 1

(x1,x2,x3,E) =

1 2 -2 1 0 0

2 -2 -1 0 1 0

2 1 2 0 0 1

r2-2r1,r3-2r1

1 2 -2 1 0 0

0 -6 3 -2 1 0

0 -3 6 -2 0 1

r2-2r3,r3*(-1/3),r1-2r3,r2*(-1/9)

1 0 2 -1/3 0 2/3

0 0 1 -2/9 -1/9 2/9

0 1 -2 2/3 0 -1/3

r1-2r2,r3+2r2,r2r3

1 0 0 1/9 2/9 2/9

0 1 0 2/9 -2/9 1/9

0 0 1 -2/9 -1/9 2/9

(x1,x2,x3)^-1 =

1/9 2/9 2/9

2/9 -2/9 1/9

-2/9 -1/9 2/9