Question

Solve system of linear equations, using matrix method, 

x – y + z = 4 

2x + y – 3z = 0 

x + y + z = 2

Answer 1

The given system can be written as AX = B, where

Thus, A is non-singular, Therefore, its inverse exists. 

Therefore, the given system is consistent and has a unique solution given by X = A ⁻¹B. 

Cofactors of A are

A₁₁ = 1 + 3 = 4, 

A₁₂ = − (2 + 3) = − 5, 

A₁₃ = 2 − 1 = 1, 

A₂₁ = − (− 1 − 1) = 2, 

A₂₂ = 1 − 1 = 0, 

A₂₃ = − (1 + 1) = − 2, 

A₃₁ = 3 − 1 = 2, 

A₃₂ = − (− 3 − 2) = 5, 

A₃₃ = 1 + 2 = 3