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Question: Answered & Verified by Expert
If the system of equations
$\begin{aligned}
& 2 x+7 y+\lambda z=3 \\
& 3 x+2 y+5 z=4 \\
& x+\mu y+32 z=-1
\end{aligned}$
has infinitely many solutions, then $(\lambda-\mu)$ is equal to________
MathematicsDeterminantsJEE MainJEE Main 2024 (06 Apr Shift 2)
Solution:
2320 Upvotes Verified Answer
The correct answer is: 38
$\begin{aligned} & \mathrm{D}=\mathrm{D}_1=\mathrm{D}_2=\mathrm{D}_3=0 \\ & \mathrm{D}_3=\left|\begin{array}{ccc}2 & 7 & 3 \\ 3 & 2 & 4 \\ 1 & \mu & -1\end{array}\right|=0 \Rightarrow \mu=-39 \\ & \mathrm{D}=\left|\begin{array}{ccc}2 & 7 & \lambda \\ 3 & 2 & 5 \\ 1 & -39 & 32\end{array}\right|=0 \Rightarrow \lambda=-1 \\ & \lambda-\mu=38\end{aligned}$

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