Question

Using properties of determinants, prove the following: |(a, a + b, a + 2b), (a + 2b, a, a + b), (a + b, a + 2b, a)| = 9b²(a + b)

Answer 1

Applying R₁ → R₁ + R₂ + R₃, we have

Taking out 3(a + b) from 1st row, we have

Applying C₁ → C₁ – C₂ and C₂ → C₂ – C₃ 

Expanding along first row, we have 

D = 3(a + b) [1. (4b² – b²)] 

= 3(a + b) x 3b² = 9b²(a + b)