જો સમીકરણ સંહિત
$ 2 x+7 y+\lambda z=3 $
$ 3 x+2 y+5 z=4 $
$ x+\mu y+32 z=-1$
ને અસંખ્ય ઉકેલો હોય, તો $(\lambda-\mu)=$...........
JEE MAIN 2024, Difficult
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$\mathrm{D}=\mathrm{D}_1=\mathrm{D}_2=\mathrm{D}_3=0$
$D_3=\left|\begin{array}{ccc}2 & 7 & 3 \\ 3 & 2 & 4 \\ 1 & \mu & -1\end{array}\right|=0 \Rightarrow \mu=-39$
$\mathrm{D}=\left|\begin{array}{ccc}2 & 7 & \lambda \\ 3 & 2 & 5 \\ 1 & -39 & 32\end{array}\right|=0 \Rightarrow \lambda=-1$
$\lambda-\mu=38$
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