If system of linear equations 2 x+3 y-z=-2 ; x+y+z=4 ; x-y+|λ| z=4 λ-4 (where

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3 and 4 .Determinants and Matrices

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If the system of linear equations $2 x+3 y-z=-2$ ; $x+y+z=4$ ; $x-y+|\lambda| z=4 \lambda-4$ (where $\lambda \in R$), has no solution, then

A

$\lambda=7$

B

$\lambda=-7$

C

$\lambda=8$

D

$\lambda^{2}=1$

(JEE MAIN-2022)

Solution

$\left|\begin{array}{ccc}2 & 3 & -1 \\ 1 & 1 & 1 \\ 1 & -1 & \mid \lambda\mid\end{array}\right|=0$

$\Rightarrow|\lambda|=7 \Rightarrow \lambda=\pm 7…….(1)$

System:

$2 x+3 y-z=-2……..(2)$

$x+y+z=4…….(3)$

$x-y+|\lambda| z=4 \lambda-4……(4)$

Eliminating y from equal $(2)$ and $(3)$ we get $x+4 z=14…..(5)$

$(3)+(4) \Rightarrow x+\left(\frac{|\lambda|+1}{2}\right) z=2 \lambda……..(6)$

Clearly for $\lambda=-7$, system is inconsistent.

Standard 12

Mathematics

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