Question

设A=(2,2,3 1,-1,0 -1,2,1)求A的逆矩阵

Answer 1

（A。E）=
[ 2 2 3 1 0 0]
[ 1 -1 0 0 1 0]
[-1 2 1 0 0 1]
初等行变换为
[ 1 -1 0 0 1 0]
[-1 2 1 0 0 1]
[ 2 2 3 1 0 0]
初等行变换为
[ 1 -1 0 0 1 0]
[ 0 1 1 0 1 1]
[ 0 4 3 1 -2 0]
初等行变换为
[ 1 0 1 0 2 1]
[ 0 1 1 0 1 1]
[ 0 0 -1 1 -6 -4]
初等行变换为
[ 1 0 0 1 -4 -3]
[ 0 1 0 1 -5 -3]
[ 0 0 -1 1 -6 -4]
初等行变换为
[ 1 0 1 0 2 1]
[ 0 1 1 0 1 1]
[ 0 0 1 -1 6 4]
A^(-1) =
[ 1 -4 -3]
[ 1 -5 -3]
[-1 6 4]