The set of equations λx−y+(cos⁡θ)z=0,3x+y+2z=0, (cos⁡θ)x+y+2z=0,0≤θ<2π, has non-trivial solution(s)

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for no value of λ and θ

for all values of λ and θ

for all values of λ and only two values of θ

for only one value of λ and all values of θ

answer is A.

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Detailed Solution

D=cos⁡θ−cos2⁡θ+6>0. Since D > 0 only trivial solution is possible.

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