$$\Delta = \left| {\matrix{ 2 & { - 3} & 5 \cr 1 & 3 & { - 1} \cr 3 & { - 1} & {{\lambda ^2} - |\lambda |} \cr } } \right| = 2\left( {3{\lambda ^2} - 3|\lambda | - 1} \right) + 3\left( {{\lambda ^2} - |\lambda | + 3} \right) + 5( - 1 - 9)$$

$$ = 9{\lambda ^2} - 9|\lambda | - 43$$

$$ = 9|\lambda {|^2} - 9|\lambda | - 43$$

$$\Delta = 0$$ for 2 values of $$|\lambda |$$ out of which one is $$-\mathrm{ve}$$ and other is $$+\mathrm{ve}$$

So, 2 values of $$\lambda$$ satisfy the system of equations to obtain no solution.