Question

求下列方阵逆矩阵1 2 32 2 13 4 3

Answer 1

1 2 3 1 0 0

2 2 1 0 1 0

3 4 3 0 0 1

r2-2r1.r3-3r1

1 2 3 1 0 0

0 -2 -5 -2 1 0

0 -2 -6 -3 0 1

r1+r2,r3-r2

1 0 -2 -1 1 0

0 -2 -5 -2 1 0

0 0 -1 -1 -1 1

r1-2r3,r2-5r3

1 0 0 1 3 -2

0 -2 0 3 6 -5

0 0 -1 -1 -1 1

(-1/2)r2,(-1)r3

1 0 0 1 3 -2

0 1 0 -3/2 -3 5/2

0 0 1 1 1 -1

所以逆矩阵为

1 3 -2

-3/2 -3 5/2

1 1 -1