设方阵A=[],AX=A-X,求矩阵X,见图片,A=135347122AX=A-X,求矩阵X,麻烦写下步骤,

Question

设方阵A=[],AX=A-X,求矩阵X,见图片,
A= 1 3 5
3 4 7
1 2 2
AX=A-X,求矩阵X ,麻烦写下步骤,

Answer 1

AX=A-X
AX+X=A
(A+I)X=A
X=(A+I)的逆*A
A+I=2 3 5 (A+I)的逆=1 0 -2
3 5 7 -2 0 0
1 2 3 1 0 1
X=(A+I)的逆*A=-1 -1 1
-2 -6 -10
2 5 7