Mathematics - Determinant Question with Solution | TestHub

For non - trivial solution.

$\mathrm{\Delta }=\left|\begin{array}{ccc}1& \lambda & -1\\ \lambda & -1& -1\\ 1& 1& -\lambda \end{array}\right|=0$

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

$\left(\lambda +1\right)-\lambda \left(1-\lambda \right) \left(1+\lambda \right)-\left(\lambda +1\right)=0$

$\lambda \left(1-\lambda \right) \left(1+\lambda \right)=0$

$\lambda =0, \lambda =1, \lambda = -1$

Exactly there value of$\lambda .$