SOLUTION: 4. Find the inverse: | 1 2 1 | | 1 1 2 |

SOLUTION: 4. Find the inverse: | 1 2 1 | | 1 1 2 | | 2 0 2 |

Question 259740: 4. Find the inverse: | 1 2 1 |
| 1 1 2 |
| 2 0 2 |
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
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.
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