If a 2 b 2 c 2 a + λ 2 b + λ 2 c + λ 2 a - λ 2 b - λ 2 c - λ 2 = k λ a 2 b 2 c 2 a b c 1 1 1 , λ ≠ 0 , then k is equal to:

Step-by-step solution

R 2 → R 2 - R 1 , R 1 → R 1 - R 3 λ 2 a - λ λ 2 b - λ λ 2 c - λ 4 a λ 4 b λ 4 c λ a - λ b - λ 2 c - λ 2 R 3 → R 3 + R 1 , R 1 → R 1 - 1 2 R 2 = - λ 2 - λ 2 - λ 2 4 a λ 4 b λ 4 c λ a 2 b 2 c 2 = 4 λ 3 1 1 1 a b c a 2 b 2 c 2 = 4 λ 3 a 2 b 2 c 2 a b c 1 1 1 ∴ K = 4 λ 2