设矩阵-4 2 0 0 2 0 0 0 0 0 -7 3 且BA=A+B,求矩阵B 0 0 5 -1

A=
-4 2 0 0
2 0 0 0
0 0 -7 3
0 0 5 -1
因为 BA=A+B
所以 B(A-E) = A
所以 B = A(A-E)^-1
A-E=
-5 2 0 0
2 -1 0 0
0 0 -8 3
0 0 5 -2
(按分块矩阵求其逆)
(A-E)^-1=
-1 -2 0 0
-2 -5 0 0
0 0 -2 -3
0 0 -5 -8
B=A(A-E)^-1 =
0 -2 0 0
-2 -4 0 0
0 0 1 -3
0 0 -5 -7