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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Determinants

If the system of equations aligned & 2 x+7 y+λ z=3 & 3 x+2 y+5 z=4...

If the system of equations 2x+7y+λz=33x+2y+5z=4x+μy+32z=−1\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 (λ−μ)(\lambda-\mu) is equal to________

Correct answer

0

Step-by-step solution

D=D1=D2=D3=0D3=∣2733241μ−1∣=0⇒μ=−39D=∣27λ3251−3932∣=0⇒λ=−1λ−μ=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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