Question

求解矩阵方程AX=X+C

Answer 1

简单计算一下即可，答案如图所示

Answer 2

AX = X+C， (A-E)X = C, X = (A-E)^(-1)C
(A-E, C) =
[1 1 0 1 2]
[1 1 1 3 4]
[0 1 1 2 1]
初等行变换为
[1 1 0 1 2]
[0 0 1 2 2]
[0 1 1 2 1]
初等行变换为
[1 1 0 1 2]
[0 1 1 2 1]
[0 0 1 2 2]
初等行变换为
[1 0 -1 -1 1]
[0 1 1 2 1]
[0 0 1 2 2]
初等行变换为
[1 0 0 1 3]
[0 1 0 0 -1]
[0 0 1 2 2]
得 X =
[1 3]
[0 -1]
[2 2]

Answer 3

AX=X十C
AX=EX十C
(A-E)X=C
解最后一个方程，就能求出解了。E是单位矩阵。