Question

大学数学，线性代数，用初等变换判定下列矩阵是否可逆，如可逆，求其逆矩阵

Answer 1

(A,E)=
[3 -2 0 -1 1 0 0 0]
[0 2 2 1 0 1 0 0]
[1 -2 -3 -2 0 0 1 0]
[0 1 2 1 0 0 0 1]
初等变换为
[1 -2 -3 -2 0 0 1 0]
[0 4 9 5 1 0 -3 0]
[0 2 2 1 0 1 0 0]
[0 1 2 1 0 0 0 1]
初等变换为
[1 -2 -3 -2 0 0 1 0]
[0 1 2 1 0 0 0 1]
[0 0 1 1 1 0 -3 -4]
[0 0 -2 -1 0 1 0 -2]
初等变换为
[1 -2 -3 -2 0 0 1 0]
[0 1 2 1 0 0 0 1]
[0 0 1 1 1 0 -3 -4]
[0 0 0 1 2 1 -6 -10]
初等变换为
[1 -2 -3 0 4 2 -11 -20]
[0 1 2 0 -2 -1 6 11]
[0 0 1 0 -1 -1 3 6]
[0 0 0 1 2 1 -6 -10]
初等变换为
[1 -2 0 0 1 -1 -2 -2]
[0 1 0 0 0 1 0 -1]
[0 0 1 0 -1 -1 3 6]
[0 0 0 1 2 1 -6 -10]
初等变换为
[1 0 0 0 1 1 -2 -4]
[0 1 0 0 0 1 0 -1]
[0 0 1 0 -1 -1 3 6]
[0 0 0 1 2 1 -6 -10]
则A可逆，逆矩阵 A^(-1)=
[ 1 1 -2 -4]
[ 0 1 0 -1]
[-1 -1 3 6]
[ 2 1 -6 -10]