$\lambda $ ની કેટલી વાસ્તવિક કિમંતો માટે સમીકરણો $2x + 4y - \lambda z = 0$ ;$4x + \lambda y + 2z = 0$ ; $\lambda x + 2y+ 2z = 0$ ને અનંત ઉકેલ મળે.
JEE MAIN 2017, Difficult
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Since the given system of linear equations has infinitely many solutions.
$\therefore \begin{array}{*{20}{c}}
2&4&{ - \lambda }\\
4&\lambda &2\\
\lambda &2&2
\end{array} = 0$
$ \Rightarrow {\lambda ^3} + 4\lambda - 40 = 0$
$\lambda $ has only $1$ real root.
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