The number of real values of for which the system of linear equat… - Vidyadip

MCQ

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
$0$
✓
$1$
C
$2$
D
$3$

✓

Answer

Correct option: B.

$1$

b
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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