If the system of equations 3 x + y + z = 1 , 6 x + 3 y + 2 z = 1 and μ x + λ y + 3 z = 1 is inconsistent, then

Question

If the system of equations 3 x + y + z = 1 , 6 x + 3 y + 2 z = 1 and μ x + λ y + 3 z = 1 is inconsistent, then, μ ≠ 9 , λ ≠ 5, μ ≠ 9 , λ = 5, μ = 9 , λ = 5, μ = 9 , λ ≠ 5

MARKS App · Accepted Answer

Δ = 3 1 1 6 3 2 μ λ 3 = 3 9 - 2 λ - 1 18 - 2 μ + 1 6 λ - 3 μ = 9 - μ Δ 1 = 1 1 1 1 3 2 1 λ 3 = 1 9 - 2 λ - 1 1 + 1 λ - 3 = 5 - λ Δ 2 = 3 1 1 6 1 2 μ 1 3 = 3 3 - 2 - 1 18 - 2 μ + 1 6 - μ = μ - 9 Δ 3 = 3 1 1 6 3 1 μ λ 1 = 3 3 - λ - 1 6 - μ + 1 6 λ - 3 μ = 3 + 3 λ - 2 μ For the system of equations to be inconsistent, Δ = 0 ⇒ μ = 9 and atleast one of Δ 1 , Δ 2 , Δ 3 is non zero ⇒ λ ≠ 5

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