Question

利用初等变换,求矩阵A={(3,2,1)， (2,2,1),(3,4,3)}的逆矩阵？

Answer 1

(A, E) =
[3,2,1,1,0,0]
[2,2,1.0,1,0]
[3,4,3,0,0,1]
初等行变换为
[3,2,1,1,0,0]
[-1,0,0.-1,1,0]
[0,2,2,-1,0,1]
初等行变换为
[1,0,0.1,-1,0]
[3,2,1,1,0,0]
[0,2,2,-1,0,1]
初等行变换为
[1,0,0.1,-1,0]
[0,2,1,-2,3,0]
[0,2,2,-1,0,1]
初等行变换为
[1,0,0.1,-1,0]
[0,2,1,-2,3,0]
[0,0,1,1,-3,1]
行变换为
[1,0,0.1,-1,0]
[0,2,0,-3,6,-1]
[0,0,1,1,-3,1]
行变换为
[1,0,0.1,-1,0]
[0,1,0,-3/2,3,-1/2]
[0,0,1,1,-3,1]
A^(-1) =
[1,-1,0]
[-3/2,3,-1/2]
[1,-3,1]