线性代数 初等变换 逆矩阵 一四两个小题

(1) (A,E) =
[ 1 1 1 1 0 0]
[ 2 -1 1 0 1 0]
[ 1 2 0 0 0 1]
行初等变换为
[ 1 1 1 1 0 0]
[ 0 -3 -1 -2 1 0]
[ 0 1 -1 -1 0 1]
行初等变换为
[ 1 0 2 2 0 -1]
[ 0 1 -1 -1 0 1]
[ 0 0 -4 -5 1 3]
行初等变换为
[ 1 0 2 -1/2 1/2 1/2]
[ 0 1 0 1/4 -1/4 1/4]
[ 0 0 1 5/4 -1/4 -3/4]
得 A^(-1) =
[-1/2 1/2 1/2]
[ 1/4 -1/4 1/4]
[ 5/4 -1/4 -3/4]
(4)
(1) (A,E) =
[ 1 3 -5 7 1 0 0 0]
[ 0 1 2 3 0 1 0 0]
[ 0 0 1 2 0 0 1 0]
[ 0 0 0 1 0 0 0 1]
行初等变换为
[ 1 3 -5 0 1 0 0 -7]
[ 0 1 2 0 0 1 0 -3]
[ 0 0 1 0 0 0 1 -2]
[ 0 0 0 1 0 0 0 1]
行初等变换为
[ 1 3 0 0 1 0 5 -17]
[ 0 1 0 0 0 1 -2 1]
[ 0 0 1 0 0 0 1 -2]
[ 0 0 0 1 0 0 0 1]
行初等变换为
[ 1 0 0 0 1 -3 11 -20]
[ 0 1 0 0 0 1 -2 1]
[ 0 0 1 0 0 0 1 -2]
[ 0 0 0 1 0 0 0 1]
得 A^(-1) =
[1 -3 11 -20]
[0 1 -2 1]
[0 0 1 -2]
[0 0 0 1]