Number of real values of λ for which system of linear equations 2x + 4y - λ z = 0

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3 and 4 .Determinants and Matrices

hard

The number of real values of $\lambda $ for which the system of linear equations $2x + 4y - \lambda z = 0$ ;$4x + \lambda y + 2z = 0$ ; $\lambda x + 2y+ 2z = 0$ has infinitely many solutions, is

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

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