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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
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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