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Question

The values of λ and μ such that the system of equations x+y+z=6, 3x+5y+5z=26, x+2y+λz=μ has no solution, are:

A
λ2, μ=10
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B
λ=3, μ10
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C
λ=3, μ=5
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D
λ=2, μ10
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Solution

The correct option is D λ=2, μ10
Δ=∣ ∣11135512λ∣ ∣=0
λ=2 and Δ1=0 for any value of μ.
For μ=10, Δ1=Δ2=Δ3=0 which corresponds to the case of infinite solutions.
μ10 for the system to be inconsistent.

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