Question

Let λ and α be real. Find the set of all values of λ for which the system of linear equations 

λx + (sinα)y + (cosα)z = 0

x + y  (cosα) + (sinα)z = 0

- x + y (sinα)y  (-cosα) z = 0

has a non-trivial solution.

For λ = 1, find all the values of α.

Answer 1

The condition for the existence of non-trivial solution (trivial solution is x = y = z = 0) is