જો સુરેખ સંહતીઓ $x+y+z =6$ ; $x+2 y+3 z =10$ ; $3 x+2 y+\lambda z =\mu$ ને બે કરતાં વધારે ઉકેલો હોય તો $\mu-\lambda^{2}$ મેળવો.
JEE MAIN 2020, Difficult
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System has intrinitely many solution
$\Rightarrow\left|\begin{array}{lll}{1} & {1} & {1} \\ {1} & {2} & {3} \\ {3} & {2} & {\lambda}\end{array}\right|=0$
$\Rightarrow \lambda=1$
$\mathrm{D}_{1}=\left|\begin{array}{ccc}{6} & {1} & {1} \\ {10} & {2} & {3} \\ {\mu} & {2} & {1}\end{array}\right|=0$
$\mu=14$
$\mu-\lambda^{2}=13$
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