设矩阵B满足AB=2B+A,其中A=|0,3,3；1,1,0；-1,2,3|,求A

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

你到底是求A还是求B啊
如果求B的话，由AB=2B+A可得(A-2E)(B-E)=AB-2B-A+2E=2E，则(B-E)/2为(A-2E)的逆矩阵，代入A，计算(A-2E)的逆矩阵，即可求出B