QJEEM21Ma6fbe: JEE Main 2021 Mathematics - Class 12 JEEM21Ma6fbe Solution: Let the system of linear equations 4x + λ y + 2z = 0 2x − y + z …

Question

Verified Solution • 2025–26 Session moderate

Let the system of linear equations

4x +

λ

y + 2z = 0

2x

-

y + z = 0

μ

x + 2y + 3z = 0,

λ

,

μ

\in

R.

has a non-trivial solution. Then which of the following is true?

Accepted Answer

Given, system of linear equations

4x + $λ$ y + 2z = 0

2x $-$ y + z = 0

$μ$ x + 2y + 3z = 0

For non-trivial solution, $Δ$ = 0

$| \begin{matrix} 4 & λ & 2 \\ 2 & - 1 & 1 \\ μ & 2 & 3 \end{matrix} | = 0$

$\Rightarrow 4 (- 3 - 2) - λ (6 - μ) + 2 (4 + μ) = 0$

$\Rightarrow - λ (6 - μ) - 2 (6 - μ) = 0$

$\Rightarrow (6 - μ) (λ + 2) = 0$

$\Rightarrow λ = - 2$ and $μ \in R$ or $μ$ = 6 and $λ \in R$ .

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