The number of real values of λ for which the system of linear...

For Infinite many solution $\Delta = 0$

i.e , \left|$\begin{cases}2 & 4 & - \lambda \\ 4 & \lambda & 2 \\ \lambda & 2 & 2\end{cases}$\right| = 0$</p><p>$⇒ 2\left(2 - 2\lambda\right) - 4\left(8 - 2\lambda\right) - \lambda\left(8 - {\lambda}^{2}\right) = 0$<br /><br />$⇒ {\lambda}^{3} + 4\lambda - 40 = 0$</p><p>$f ( x ) = {x}^{3} + 4x - 40$is strictly increasing</p><p>i.e., equation has only one real root,<br /><br />Also,${∆}_{1} = 0$,${∆}_{2} = 0$,${∆}_{3} = 0$<br /><br />$∴$Only one value of$\lambda is possible