If the system of equations x + y + z = 6 ,   x + 2 y + λ z = 10 and x + 2 y + 3 z = μ has infinite solutions, then the value of λ + 2 μ is equal to

Step-by-step solution

For infinite solutions, Δ = Δ 1 = Δ 2 = Δ 3 = 0 Δ = 1 1 1 1 2 λ 1 2 3 = 1 6 - 2 λ - 1 3 - λ + 0 = 0 ⇒ λ = 3 Δ 1 = 6 1 1 10 2 λ μ 2 3 = 0 ⇒ 6 6 - 2 λ - 1 30 - 4 λ + 1 20 - 2 μ = 0 ∵ λ = 3 ⇒ μ = 1 0 Δ 2 = 1 6 1 1 10 3 1 10 3 = 0 , Δ 3 = 1 1 6 1 2 10 1 2 10 = 0 λ + 2 μ = 2 3