Question

求大神解答一道线性代数题，在线等，急！

问题在图上

Answer 1

AX = A+ X, (A-E)X = A, X = (A-E)^(-1)A
(A-E, A) =
[ 1 2 3 2 2 3]
[ 1 0 0 1 1 0]
[-1 2 2 -1 2 3]
初等行变换为
[ 1 0 0 1 1 0]
[ 0 2 3 1 1 3]
[ 0 2 2 0 3 3]
初等行变换为
[ 1 0 0 1 1 0]
[ 0 1 1 0 3/2 3.2]
[ 0 0 1 1 -2 0]
初等行变换为
[ 1 0 0 1 1 0]
[ 0 1 0 -1 7/2 3/2]
[ 0 0 1 1 -2 0]
X =
[ 1 1 0]
[-1 7/2 3/2]
[ 1 -2 0]

Answer 2

简单计算一下，答案如图所示