If system of equations 2 x+7 y+λ z=3 3 x+2 y+5 z=4 x+μ y+32 z=-1 has infinitely many solutions, th

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3 and 4 .Determinants and Matrices

hard

If the system of equations

$ 2 x+7 y+\lambda z=3 $

$ 3 x+2 y+5 z=4 $

$ x+\mu y+32 z=-1$

has infinitely many solutions, then $(\lambda-\mu)$ is equal to $\qquad$

A

$38$

B

$39$

C

$34$

D

$15$

(JEE MAIN-2024)

Solution

$\mathrm{D}=\mathrm{D}_1=\mathrm{D}_2=\mathrm{D}_3=0$

$D_3=\left|\begin{array}{ccc}2 & 7 & 3 \\ 3 & 2 & 4 \\ 1 & \mu & -1\end{array}\right|=0 \Rightarrow \mu=-39$

$\mathrm{D}=\left|\begin{array}{ccc}2 & 7 & \lambda \\ 3 & 2 & 5 \\ 1 & -39 & 32\end{array}\right|=0 \Rightarrow \lambda=-1$

$\lambda-\mu=38$

Standard 12

Mathematics

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