Answer :

The given system of equations is:

x - y + 2z = 7

3x + 4y - 5z = -5

2x – y + 3z = 12

The given system of equations can be written in the form of AX = B, where

Now |A| = 1(12-5) + 1(9+10) + 2(-3-8) = 4 ≠ 0

∴ A is a non-singular matrix and hence A^{-1} exists.

Now A_{11} = 7, A_{12} = -19, A_{13} = -11, A_{21} = 1, A_{22} = -1, A_{23} = -1, A_{31} = -3, A_{32} = 11, A_{33} = 7

So AdjA =

∴

So

Hence

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