Question

Solve the system of equations:

2/x + 3/y + 10/z = 4

4/x - 6/y + 5/z = 1

6/x + 9/y - 20/z = 2

Answer 1

Let 1/x = p, 1/y = q and 1/z = r,  then the given equations become 

2p + 3q + 10r = 4, 4p − 6q + 5r = 1, 6p + 9q − 20r = 2 

This system can be written as AX = B, where

Thus, A is non-singular. Therefore, its inverse exists. Therefore, the above system is consistent and has a unique solution given by X = A ⁻¹B 

Cofactors of A are 

A₁₁ = 120 − 45 = 75,

A₁₂ = − ( − 80 − 30) = 110, 

A₁₃ = (36 + 36) = 72, 

A₂₁ = − ( − 60 − 90) = 150, 

A₂₂ = ( − 40 − 60) = − 100, 

A₂₃ = − (18 − 18) = 0, 

A₃₁ = 15 + 60 = 75, 

A₃₂ = − (10 − 40) = 30, 

A₃₃ = − 12 − 12 = − 24