Question

最下面的矩阵,求其逆矩阵,用初等行变换怎么做,-6该怎么解决,可以提出-1/6么

Answer 1

(P, E) =

[ 1 0 0 0 1 0 0 0]

[ 0 1 0 0 0 1 0 0]

[-1 0 1 0 0 0 1 0]

[ 0 3 0 -6 0 0 0 1]

行初等变换为

[ 1 0 0 0 1 0 0 0]

[ 0 1 0 0 0 1 0 0]

[ 0 0 1 0 1 0 1 0]

[ 0 0 0 -6 0 -3 0 1]

行初等变换为

[ 1 0 0 0 1 0 0 0]

[ 0 1 0 0 0 1 0 0]

[ 0 0 1 0 1 0 1 0]

[ 0 0 0 1 0 1/2 0 -1/6]

得 P^（-1）=

[1 0 0 0]

[0 1 0 0]

[1 0 1 0]

[0 1/2 0 -1/6].