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

Algebra ->  Algebra  -> Permutations -> SOLUTION: 4. Find the inverse: | 1 2 1 | | 1 1 2 | | 2 0 2 |      Log On

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Permutations 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.