Question

线性代数题求过程

线性代数题求过程计算证明题的第二题

Answer 1

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