7. (A, E) =
[1 2 3 1 0 0]
[2 1 2 0 1 0]
[1 3 3 0 0 1]
初等行变换为
[1 2 3 1 0 0]
[0 -3 -4 -2 1 0]
[0 1 0 -1 0 1]
初等行变换为
[1 2 3 1 0 0]
[0 1 0 -1 0 1]
[0 -3 -4 -2 1 0]
初等行变换为
[1 0 3 3 0 -2]
[0 1 0 -1 0 1]
[0 0 -4 -5 1 3]
初等行变换为
[1 0 0 -3/4 3/4 1/4]
[0 1 0 -1 0 1]
[0 0 1 5/4 -1/4 -3/4]
A^(-1) =
[-3/4 3/4 1/4]
[ -1 0 1]
[ 5/4 -1/4 -3/4]
跟E写一起再做变换就行了