线性代数求解矩阵方程

化简之后乘过去

等式两边同时左乘A的-1次方

AX = 2X+A, (A-2E)X = A, X = (A-2E)^(-1)A,
[A-2E, A] =
[-1 0 0 1 0 0]
[-1 -1 3 -1 1 3]
[ 0 2 -3 0 2 -1]
初等行变换为
[ 1 0 0 -1 0 0]
[ 0 -1 3 -2 1 3]
[ 0 2 -3 0 2 -1]
初等行变换为
[ 1 0 0 -1 0 0]
[ 0 1 -3 2 -1 -3]
[ 0 0 3 -4 4 5]
初等行变换为
[ 1 0 0 -1 0 0]
[ 0 1 0 -2 3 2]
[ 0 0 1 -4/3 4/3 5/3]
X =
[ -1 0 0]
[ -2 3 2]
[-4/3 4/3 5/3]