Question

用初等变换方法求解矩阵方程，两道题如图

Answer 1

1. （A， B) =
[1 2 -1 0 1]
[3 4 -2 1 2]
[5 -4 1 2 3]
初等行变换为
[1 2 -1 0 1]
[0 -2 1 1 -1]
[0 -14 6 2 -2]
初等行变换为
[1 0 0 1 0]
[0 1 -1/2 -1/2 1/2]
[0 0 -1 -5 5]
初等行变换为
[1 0 0 1 0]
[0 1 0 2 -2]
[0 0 1 5 -5]
得 X =
[ 1 0]
[ 2 -2]
[ 5 -5]

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