第一行1,2,3 4二行0 ,1,2,3三行0,0,1,2四行0,0,0,1用初等行变换法求该可逆矩阵的逆矩阵,
问题描述：
第一行1,2,3 4二行0 ,1,2,3三行0,0,1,2四行0,0,0,1用初等行变换法求该可逆矩阵的逆矩阵,
答
(A,E) =
1 2 3 4 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
r1-4r4,r2-3r4,r3-2r4
1 2 3 0 1 0 0 -4
0 1 2 0 0 1 0 -3
0 0 1 0 0 0 1 -2
0 0 0 1 0 0 0 1
r1-3r2,r1-2r2
1 2 0 0 1 0 -3 2
0 1 0 0 0 1 -2 1
0 0 1 0 0 0 1 -2
0 0 0 1 0 0 0 1
r1-2r2
1 0 0 0 1 -2 1 0
0 1 0 0 0 1 -2 1
0 0 1 0 0 0 1 -2
0 0 0 1 0 0 0 1
A^-1 =
1 -2 1 0
0 1 -2 1
0 0 1 -2
0 0 0 1