Find the inverse of the matrix 1    2    -1 3    7    -1 -5   -7   -15The Answer is   -175   37   -13, 95   -20   7, 14   -3   1 SHOW THE STEP-BY-STEP. PLEASE  

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sciencesolve eNotes educator| Certified Educator

You need to evaluate the determinant of the matrix to check if there exists a inverse for the given matrix, such that:

`det A = [(1,2,-1),(3,7,-1),(-5,-7,-15)] = -26 != 0`

Since the determinant of the matrix is different from zero, you may evaluate its inverse, such that:

`A^(-1) = 1/(det A)*[(a_(11),a_(21),a_(31)),(a_(12),a_(22),a_(32)),(a_(13),a_(23),a_(33))]`

`A^*= [(a_(11),a_(21),a_(31)),(a_(12),a_(22),a_(32)),(a_(13),a_(23),a_(33))]`

`a_(11) = -112`

`a_(12) = 50`

`a_(13) = 14`

`a_(21) = 37`

`a_(22) = -20`

`a_(23) = -3`

`a_(31) = 5`

`a_(32) = -2`

`A^*` =` [(-112,37,5),(50,-20,-2),(14,-3,1)]`

`A^(-1) = (-1/26)*` `[(-112,37,5),(50,-20,-2),(14,-3,1)]`