Question

求矩阵a=1 -1 1 2 1 0 2 1 -1的逆矩阵？

快啊在考试呢

Answer 1

使用初等行变换，(A,E)=
1 -1 1 1 0 0
2 1 0 0 1 0
2 1 -1 0 0 1 r3-r2,r2-2r1
~
1 -1 1 1 0 0
0 3 -2 -2 1 0
0 0 -1 0 -1 1 r1+r3,r2-2r3,r3*-1
~
1 -1 0 1 -1 1
0 3 0 -2 3 -2
0 0 1 0 1 -1 r2/3,r1+r2
~
1 0 0 1/3 0 1/3
0 1 0 -2/3 1 -2/3
0 0 1 0 1 -1
这样化简得到E,A^-1，即A的逆矩阵为
1/3 0 1/3
-2/3 1 -2/3
0 1 -1