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Question

The set of all values of λ for which the system of linear equations
x2y2z=λx
x+2y+z=λy
xy=λz
has a non-trivial solution :

A
is a singleton
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B
is an empty set
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C
contains exactly two elements
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D
contains more than two elements
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Solution

The correct option is A is a singleton
For non-trivial solution, Δ=0

∣ ∣1λ2212λ111λ∣ ∣=0

R2R2+R3
∣ ∣1λ2201λ1λ11λ∣ ∣=0

(1λ)∣ ∣1λ2201111λ∣ ∣=0

Expanding along R2, we get
(1λ)(λ22λ+1)=0
(1λ)(λ1)2=0
λ=1

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