已知矩阵A=101,1-10,012．B=301,110,014,求A的逆矩阵A^-1

Question

已知矩阵A=1 0 1,1 -1 0,0 1 2．B=3 0 1,1 1 0,0 1 4,求A的逆矩阵A^-1

Answer 1

(A,E) =
1 0 1 1 0 0
1 -1 0 0 1 0
0 1 2 0 0 1
r2-r1
1 0 1 1 0 0
0 -1 -1 -1 1 0
0 1 2 0 0 1
r3+r2
1 0 1 1 0 0
0 -1 -1 -1 1 0
0 0 1 -1 1 1
r1-r3,r2+r3
1 0 0 2 -1 -1
0 -1 0 -2 2 1
0 0 1 -1 1 1
r2*(-1)
1 0 0 2 -1 -1
0 1 0 2 -2 -1
0 0 1 -1 1 1
所以 A^-1 =
2 -1 -1
2 -2 -1
-1 1 1