Question

求行列式的逆矩阵 1 1 -1 0 2 2 1 -1 0

Answer 1

题目有误,不是行列式的逆矩阵,而是矩阵的逆矩阵.
（A,E）=
[1 1 -1 1 0 0]
[0 2 2 0 1 0]
[1 -1 0 0 0 1]
行初等变换为
[1 1 -1 1 0 0]
[0 2 2 0 1 0]
[0 -2 1 -1 0 1]
行初等变换为
[1 1 -1 1 0 0]
[0 2 2 0 1 0]
[0 0 3 -1 1 1]
行初等变换为
[1 1 0 2/3 1/3 1/3]
[0 2 0 2/3 1/3 -2/3]
[0 0 1 -1/3 1/3 1/3]
行初等变换为
[1 0 0 1/3 1/6 2/3]
[0 1 0 1/3 1/6 -1/3]
[0 0 1 -1/3 1/3 1/3]
得逆矩阵 A^(-1)=
[ 1/3 1/6 2/3]
[ 1/3 1/6 -1/3]
[-1/3 1/3 1/3]