If the system of linear equations x + y + z = 5 , x + 2 y + 2 z = 6 , x + 3 y + λ z = µ , ( λ , µ ∈ R ) , has infinitely many solutions, then the value of λ + µ is:

Question

If the system of linear equations x + y + z = 5 , x + 2 y + 2 z = 6 , x + 3 y + λ z = µ , ( λ , µ ∈ R ) , has infinitely many solutions, then the value of λ + µ is:, 7, 10, 12, 9

MARKS App · Accepted Answer

∆ = 1 1 1 1 2 2 1 3 λ = λ - 3 ∆ 1 = 5 1 1 6 2 2 μ 3 λ = 4 λ - 3 ∆ 3 = 1 5 1 1 6 2 1 μ λ = λ - μ + 4 ∆ 4 = 1 1 5 1 2 6 1 3 μ = μ - 7 For infinite many solution ∆ = ∆ 1 = ∆ 2 = ∆ 3 = 0 ⇒ λ = 3 , & μ = 7 from ∆ = 0 & ∆ 4 = 0 & λ = 3 , μ = 7 Satisfies ∆ 3 = 0 = ∆ 1 ∴ λ + μ = 10

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