1.
Let SS denote the set of all real values of λ\lambda such that the system of equations
λx+y+z=1\lambda x + y + z = 1

x+λy+z=1x + \lambda y + z = 1

x+y+λz=1x + y + \lambda z = 1

is inconsistent. Then ∑λ∈S(∣λ∣2+∣λ∣)\sum_{\lambda \in S} (|\lambda|^2 + |\lambda|) is equal to: