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 A₁₁ = 7, A₁₂ = -19, A₁₃ = -11, A₂₁ = 1, A₂₂ = -1, A₂₃ = -1, A₃₁ = -3, A₃₂ = 11, A₃₃ = 7

So AdjA =

∴

So

Hence