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3 and 4 .Determinants and Matrices
normal
If the system of equation $2x + 3y =\, -1; 3x + y = 2; \lambda x + 2y = \mu $ is consistent, then
A
$\lambda - \mu = 2$
B
$\lambda + \mu = -1$
C
$\lambda + \mu = 3$
D
$\lambda - \mu + 8= 0$
Solution
Solve equation $( 1)$ and $(2)$ we get
$\mathrm{x}=1$ and $\mathrm{y}=-1$ put in equation $(3)$
$\lambda \mathrm{x}+2 \mathrm{y}=\mu \Rightarrow \lambda-2=\mu$
$\Rightarrow \quad \boxed{\lambda – \mu = 2}$
Standard 12
Mathematics