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Question

The set of equations
λxy+(cosθ)z=0
3x+y+2z=0
(cosθ)x+y+2z=0,
where 0θ<2π, has non-trivial solutions for

A
all values of λ and θ
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B
no value of λ and θ
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C
all values of λ and only two values of θ
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D
only one value of λ and all values of θ
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Solution

The correct option is B no value of λ and θ
The system of equations has non-trivial solutions iff
∣ ∣λ1cosθ312cosθ12∣ ∣=0

62cosθ+cosθ(3cosθ)=0
cosθcos2θ+6=0
LHS >0 for all θ as |cosθ|1
So, the system of equations cannot have non-trivial solutions for any value of λ and θ

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