Matrices And Determinants

Let \(S\) denote the set of all real values of \(\lambda\) such that the system of equations

\(\lambda x+y+z=1\)

\(x+\lambda y+z=1\)

\(x+y+\lambda z=1\)

is inconsistent, then \(\sum_\limits{\lambda \in S}\left(|\lambda|^{2}+|\lambda|\right)\) is equal to