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3 and 4 .Determinants and Matrices
hard
यदि रैखिक समीकरण निकाय $x+y+z=6$, $x+2 y+3 z=10$, $3 x+2 y+\lambda z=\mu$ के दो से अधिक हल हैं, तो $\mu-\lambda^{2}$ बराबर है
A
$11$
B
$12$
C
$13$
D
$15$
(JEE MAIN-2020)
Solution
System has intrinitely many solution
$\Rightarrow\left|\begin{array}{lll}{1} & {1} & {1} \\ {1} & {2} & {3} \\ {3} & {2} & {\lambda}\end{array}\right|=0$
$\Rightarrow \lambda=1$
$\mathrm{D}_{1}=\left|\begin{array}{ccc}{6} & {1} & {1} \\ {10} & {2} & {3} \\ {\mu} & {2} & {1}\end{array}\right|=0$
$\mu=14$
$\mu-\lambda^{2}=13$
Standard 12
Mathematics
