Question

Using matrix method, solve the following system of equations: x + 2y + z = 7, x + 3z = 11, 2x – 3y = 1

Answer 1

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

Now

= 9 + 12 – 3 = 18 ≠ 0 

Non-singular matrix.

A₁₁ = (0 + 9) = 9, A₁₂ = -(0 – 6) = 6, A₁₃ = (-3 – 0) = -3 

A₂₁ = – (0 + 3) = -3, A₂₂ = (0 – 2) = -2 

A₂₃ = -(-3 – 4) = 7 

A₃₁ = (6 – 0) = 6, A₃₂ = -(-3 – 1) = -2, A₃₃ = (0 – 2) = -2

Thus x = 2, y = 1 and z = 3.