Solve system of linear equations, using matrix method.

The given system of equations is:

2x + y + z = 1

0x + 3y - 5z = 9

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

Now |A| = 2(10+3)-1(-5) +1(3) = 34 ≠ 0

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

Now A₁₁ = 13, A₁₂ = 5, A₁₃ = 3, A₂₁ = 8, A₂₂ = -10, A₂₃ = -6, A₃₁ = 1, A₃₂ = 3, A₃₃ = -5

So AdjA =

∴

And hence X = A^-1B

So

Hence