Question

求简单三阶矩阵的逆矩阵

图片里的题目，谢谢大神！求详细步骤，初学者很多不懂的。

Answer 1

(A, E) =
[ 0 -2 1 1 0 0]
[ 3 0 -2 0 1 0]
[-2 3 0 0 0 1]
交换 2，3 行，初等行变换为
[ 3 0 -2 0 1 0]
[ 0 -2 1 1 0 0]
[-2 3 0 0 0 1]
第 3 行加到第 1 行，初等行变换为
[ 1 3 -2 0 1 1]
[ 0 -2 1 1 0 0]
[-2 3 0 0 0 1]
第 1 行 2 倍加到第 3行，初等行变换为
[ 1 3 -2 0 1 1]
[ 0 -2 1 1 0 0]
[ 0 9 -4 0 2 3]
初等行变换为
[ 1 0 -1/2 3/2 1 1]
[ 0 1 -1/2 -1/2 0 0]
[ 0 0 1/2 9/2 2 3]
初等行变换为
[ 1 0 0 6 3 4]
[ 0 1 0 4 2 3]
[ 0 0 1 9 4 6]
A^(-1) =
[6 3 4]
[4 2 3]
[9 4 6]