Question

利用初等变换求矩阵的逆矩阵第一行1 1 1第二行2 -1 1第三行1 2 0,

Answer 1

解: (A,E) =
1 1 1 1 0 0
2 -1 1 0 1 0
1 2 0 0 0 1
r2-2r1,r3-r1
1 1 1 1 0 0
0 -3 -1 -2 1 0
0 1 -1 -1 0 1
r1-r3,r2+3r3
1 0 2 2 0 -1
0 0 -4 -5 1 3
0 1 -1 -1 0 1
r2*(-1/4),r1-2r2,r3+r2
1 0 0 -1/2 1/2 1/2
0 0 1 5/4 -1/4 -3/4
0 1 0 1/4 -1/4 1/4
r2r3
1 0 0 -1/2 1/2 1/2
0 1 0 1/4 -1/4 1/4
0 0 1 5/4 -1/4 -3/4
A^-1 =
-1/2 1/2 1/2
1/4 -1/4 1/4
5/4 -1/4 -3/4