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$\lambda^{2}=1$
$\Rightarrow|\lambda|=7 \Rightarrow \lambda=\pm 7.......(1)$
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.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.