The set of all values of λ for which the system of linear equations x - 2 y - 2 z = λ x x + 2 y + z = λ y - x - y = λ z has a non-trivial solution :

Step-by-step solution

For non-trivial solution, ∆ = 0 . ⇒ 1 - λ - 2 - 2 1 2 - λ 1 - 1 - 1 - λ = 0 ⇒ 1 - λ - 2 λ + λ 2 + 1 + 1 - λ + 1 - 1   - 1 + 2 - λ = 0 ⇒ λ 2 - 3 λ 2 + 3 λ - 1 = 0 ⇒ λ - 1 3 = 0 ⇒ λ = 1 Singleton set