Let λand α be real. The set of all values of for which the system of linear equationsλx+(sinα)y+(cosα)z=0,x+(cosα)y+(sinα)z=0,−x+(sinα)y−(cosα)z=0has a non-trival solution is

The condition for a homogeneour system of equations to have a non-trivial solution is Δ=0 ⇒Δ=λsinαcosα1cosαsinα-1sinα-cosα=0 ⇒λ-cos2α-sin2α-sinα-cosα+sinα+cosαsinα+cosα=0 ⇒λ=cos2α+sin2α The range of cos2α+sin2α is -2,2. ∴The range of λ is -2,2