Question

利用初等变换求矩阵的逆矩阵B= 161 330 -102

Answer 1

写出B，E=
1 6 1 1 0 0
3 3 0 0 1 0
-1 0 2 0 0 1 r1+r3，r2/3
~
0 6 3 1 0 1
1 1 0 0 1/3 0
-1 0 2 0 0 1 r3+r2，r1/6，r2-r1
~
0 1 1/2 1/6 0 1/6
1 0 -1/2 -1/6 1/3 -1/6
0 1 2 0 1/3 1 r3-r1，交换r1r2
~
1 0 -1/2 -1/6 1/3 -1/6
0 1 1/2 1/6 0 1/6
0 0 3/2 -1/6 1/3 5/6 r3/1.5，r1+0.5r3，r2-0.5r3
~
1 0 0 -2/9 4/9 1/9
0 1 0 2/9 -1/9 -1/9
0 0 1 -1/9 2/9 5/9
于是得到了(E，A^-1)
即A的逆矩阵为
-2/9 4/9 1/9
2/9 -1/9 -1/9
-1/9 2/9 5/9