Question

Using matrices, solve the following system of equations: 

x – y + z = 4; 

2x + y – 3z = 0; 

x + y + z = 2

Answer 1

Given equations 

x – y + z = 4 

2x + y – 3z = 0 

x + y + z = 2 

We can write this system of equations as AX = B where

= 1(1 + 3) - (- 1) (2 + 3) + 1 (2 - 1) = 4 + 5 + 1 = 10 

∴ A^–1 exists. 

A₁₁ = 4, A₁₂ = –5, A₁₃ = 1 

A₂₁ = 2, A₂₂ = 0, A₂₃ = –2 

A₃₁ = 2, A₃₂ = 5, A₃₃ = 3

The required solution is 

∴ x = 2, y = - 1, z = 1