Let α, β, γ be three real numbers and A=1cos⁡(β−α)cos⁡(γ−α)cos⁡(α−β)1cos⁡(γ−β)cos⁡(α−γ)cos⁡(β−γ)1 then

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Ais singular

Ais non-singular

Ais orthogonal

none of these

answer is A.

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Detailed Solution

|A|=1cos⁡(β−α)cos⁡(γ−α)cos⁡(α−β)1cos⁡(γ−β)cos⁡(α−γ)cos⁡(β−γ)1=cos⁡αsin⁡α0cos⁡βsin⁡β0cos⁡γcos⁡γ0cos⁡αsin⁡α0cos⁡βsin⁡β0cos⁡γsin⁡γ0=0⇒ A is singular.

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