Question

Solve the following system of linear equations by matrix method:

3x - 2y + 3z = 8

2x + y - z = 1

4x - 3y + 2z = 4

Answer 1

The system of equations can be written in the form A X = B where

|A| = 3(2 - 3) + 2(4 + 4) + 3(-6 -4) = -17

Hence, A is non singular matrix and so its inverse exists. Now

A₁₁ = -1 A₁₂ = -8 A₁₃ = -10

A₂₁ = -5 A₂₂ = -6 A₂₃ = +1

A₃₁ = -1 A₃₂ = +9 A₃₃ = +7