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3 and 4 .Determinants and Matrices
hard
$\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.
A
$0$
B
$1$
C
$2$
D
$3$
(JEE MAIN-2017)
Solution
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.
Standard 12
Mathematics
