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 and so its inverse exists. Now

A₁₁ = -1, A₁₂ = -8, A₁₃ = -10

A₂₁ = -5, A₂₂ = -6, A₂₃ = +1

A₃₁ = -1, A₃₂ = +9, A₃₃ = +7

A^-1 = 1/|A| adj A