怎么求矩阵的逆矩阵题目A=(033,110,-123)AB=A+2B求B

Question

怎么求矩阵 的逆矩阵　题目　A=(0 3 3,1 1 0,-1 2 3)　AB=A+2B 求B

Answer 1

由 AB=2B+A 得 (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+r2
0 1 3 2 5 3
1 -1 0 1 1 0
0 1 1 0 3 3
r2+r1,r3-r1
0 1 3 2 5 3
1 0 3 3 6 3
0 0 -2 -2 -2 0
r3*(-1/2),r1-3r3,r2-3r3
0 1 0 -1 2 3
1 0 0 0 3 3
0 0 1 1 1 0
交换行
1 0 0 0 3 3
0 1 0 -1 2 3
0 0 1 1 1 0
B =
0 3 3
-1 2 3
1 1 0