QJEEM22Mabadc: JEE Main 2022 Mathematics - Class 12 JEEM22Mabadc Solution: The number of real values of λ , such that the system of linear …

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QJEEM22Mabadc: JEE Main 2022 Mathematics - Class 12 JEEM22Mabadc Solution: The number of real values of λ , such that the system of linear …

The number of real values of $λ$ , such that the system of linear equations

2x $-$ 3y + 5z = 9

x + 3y $-$ z = $-$ 18

3x $-$ y + ( $λ$ ² $-$ | $λ$ |)z = 16

has no solutions, is

Multiple Choice Options

A 0
B 1
C 2
D 4

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Accepted Answer

$Δ = | \begin{matrix} 2 & - 3 & 5 \\ 1 & 3 & - 1 \\ 3 & - 1 & λ^{2} - | λ | \end{matrix} | = 2 (3 λ^{2} - 3 | λ | - 1) + 3 (λ^{2} - | λ | + 3) + 5 (- 1 - 9)$

$= 9 λ^{2} - 9 | λ | - 43$

$= 9 | λ |^{2} - 9 | λ | - 43$

$Δ = 0$ for 2 values of $| λ |$ out of which one is $- ve$ and other is $+ ve$

So, 2 values of $λ$ satisfy the system of equations to obtain no solution.

QJEEM22Mabadc: JEE Main 2022 Mathematics - Class 12 JEEM22Mabadc Solution: The number of real values of λ , such that the system of linear …

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