Question

Examine the consistency of the system of equations.

x + y + z = 1

2x + 3y + 2z = 2

ax + ay + 2az = 4

Answer 1

Let, A = `[(1,1,1),(2,3,2),(a,a,2a)]`, X = `[(x),(y),(z)]`, B = `[(1),(2),(4)]`

|A| = `|(1,1,1),(2,3,2),(a,a,2a)|`

= 1 × (3 × 2a − a × 2) − 1 × (2 × 2a − a × 2) + 1 × (2 × a − a × 3)

= 4a − 2a − a

= a ≠ 0

Hence, the system of equations is consistent.