If the system of linear equations 2 x+3 y-z=-2 ; x+y+z=4 ; x-y+| … - Vidyadip

MCQ

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
$\lambda=7$
✓
$\lambda=-7$
C
$\lambda=8$
D
$\lambda^{2}=1$

✓

Answer

Correct option: B.

$\lambda=-7$

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

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

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.

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