Question

求矩阵麻烦具体一点,已知A=＜0 3 3,1 1 0,-1 2 3＞,且有AB=A+2B,求B

Answer 1

因为 AB=A+2B所以 (A-2E)B=A

(A-2E,A) =

-2 3 3 0 3 3

1 -1 0 1 1 0

-1 2 1 -1 2 3

r1+2r2,r3+r20 1 3 2 5 3

1 -1 0 1 1 0

0 1 1 0 3 3

r1-r3,r2+r30 0 2 2 2 0

1 0 1 1 4 3

0 1 1 0 3 3

r1*(1/2),r2-r1,r3-r10 0 1 1 1 0

1 0 0 0 3 3

0 1 0 -1 2 3

交换行1 0 0 0 3 3

0 1 0 -1 2 3

0 0 1 1 1 0

所以 B= 0 3 3

-1 2 3

1 1 0