- Home
- Standard 12
- Mathematics
3 and 4 .Determinants and Matrices
medium
यदि रेखीय समीकरणों का निकाय
$2 x+3 y-z=-2$
$x+y+z=4$
$x-y+|\lambda| z=4 \lambda-4$
जहाँ $\lambda \in R$, का कोई हल ना हो, तब
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
