The given system of equations is:

x - y + z = 4

2x + y -3z = 0

x + y + z = 2

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

Now |A| = 1(1+3) + 1(5) + 1(1) = 10 ≠ 0

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

Now A₁₁ = 4, A₁₂ = -5, A₁₃ = 1, A₂₁ = 2, A₂₂ = 0, A₂₃ = -2, A₃₁ = 1, A₃₂ = -2, A₃₃ = 3

So AdjA =

And hence X = A^-1B

So

Hence x = 2, y = -1 and z = 1.