Question

用逆矩阵求解矩阵方程

Answer 1

(1) AX = B, 则 X = A^(-1)B, A^(-1) =
[ 3 -5]
[-1 2]
X = A^(-1)B =
[2 -23]
[0 8]
(2) XA = B, 则 X = BA^(-1), (A, E) =
[2 1 -1 1 0 0]
[2 1 0 0 1 0]
[1 -1 1 0 0 1]
初等行变换为
[1 -1 1 0 0 1]
[0 3 -3 1 0 -2]
[0 3 -2 0 1 -2]
初等行变换为
[1 0 0 1/3 0 1/3]
[0 1 -1 1/3 0 -2/3]
[0 0 1 -1 1 0]
初等行变换为

[1 -1 1 0 0 1]
[0 3 -3 1 0 -2]
[0 0 1 -1 1 0]
初等行变换为
[1 0 0 1/3 0 1/3]
[0 1 0 -2/3 1 -2/3]
[0 0 1 -1 1 0]
A^(-1) =
[ 1/3 0 1/3]
[-2/3 1 -2/3]
[ -1 1 0]
X = BA^(-1) =
[-2 2 1]
[-8/3 5 -2/3]
(3) AXB = C, X = A^(-1)CB^(-1)
仿上做即可。

Answer 2

很简单呀