Question

求行列式的逆矩阵1 1 -10 2 21 -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]