The system of linear equations x + - z = 0 - y - z = 0 x + y - = 0...

For non - trivial solution.

\Delta = \left|\begin{cases}1 & \lambda & - 1 \\ \lambda & - 1 & - 1 \\ 1 & 1 & - \lambda\end{cases}\right| = 0

$1\left(\lambda + 1\right) - \lambda\left(- {\lambda}^{2} + 1\right) - 1\left(\lambda + 1\right) = 0$

\left(\lambda + 1\right) - \lambda\left(1 - \lambda\right)\left(1 + \lambda\right) - \left(\lambda + 1\right) = 0$<br/><br/>$\lambda\left(1 - \lambda\right)\left(1 + \lambda\right) = 0$<br/><br/>$\lambda = 0, \lambda = 1, \lambda = - 1$<br/><br/>Exactly there value of$\lambda .