Question 259740
The inverse is
l 1/2 . . . -1 . . . . 3/4 . . . l
l 1/2 . . . . 0. . . . .-1/4 . . l
l-1/2 . . . 1 . . . . . -1/4 . . l
here is the idea of how I got this. Set the original matrix = to identity matrix
| 1 2 1 | 1 0 0 l
| 1 1 2 | 0 1 0 l
| 2 0 2 | 0 0 1 l
step 1 - row 2 - row 1 into row 2; row 3 - 2x row 1 into row 3 to get 
| 1   2 1 |    1 0 0 l
| 0 -1 1 | -1 1 0 l
| 0 -4 0 |  -2 0 1 l
step 2 - change all signs of row 2 to get
| 1   2 1 |  1   0 0 l
| 0   1 1 |  1 -1 0 l
| 0 -4 0 | -2  0 1 l
step 3 - row 1 - 2x row 2 into row 1 ; row 3 + 4x row 2 into row 3 to get
| 1   0   3 |  -1   2    0 l
| 0   1 -1 |   1 -1     0 l
| 0   0 -4 |   2  -4 -1 l
step 4 - divide row 3 by -4 to get
| 1   0   3 |      -1      2     0 l
| 0   1 -1 |        1   -1      0 l
| 0   0   1 |   -1/2  -1 -1/4 l
step 5 - row - 3x row 3 into row 1 ; row 2 + row 3 into row 2 to get
| 1  0  0 |     1/2  -1    0     l
| 0  1  0 |     1/2    0  -1/4 l
| 0  0  1 |  -1/2  -1  -1/4 l
this gives us the inverse.