(A,E) =
0 0 1 0 1 0 0 0
0 0 0 2 0 1 0 0
3 0 0 0 0 0 1 0
0 4 0 0 0 0 0 1
r2*(1/2),r3*(1/3),r4*(1/4)
0 0 1 0 1 0 0 0
0 0 0 1 0 1/2 0 0
1 0 0 0 0 0 1/3 0
0 1 0 0 0 0 0 1/4
交换行
1 0 0 0 0 0 1/3 0
0 1 0 0 0 0 0 1/4
0 0 1 0 1 0 0 0
0 0 0 1 0 1/2 0 0
所以 A^-1 =
0 0 1/3 0
0 0 0 1/4
1 0 0 0
0 1/2 0 0
分块矩阵的方法:
A =
0 B
C 0
B,C都是2阶的对角矩阵
其逆为对角线上元素取倒数构成的对角矩阵
所以 A^-1 =
0 C^-1
B^-1 0
=
0 0 1/3 0
0 0 0 1/4
1 0 0 0
0 1/2 0 0