If the 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, then (λ-μ) is equal to

Mathematics · Determinants

JEE Main 2024 — 6 April, Shift 2 — Question 29

If the system of equations

$2 \mathrm{x}+7 \mathrm{y}+\lambda \mathrm{z}=3$

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

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

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

Numerical answer — enter this value.

$\mathrm{D}=\mathrm{D}_{1}=\mathrm{D}_{2}=\mathrm{D}_{3}=0$

${{D}_{3}}=\left| \begin{matrix}2 & 7 & 3 \\3 & 2 & 4 \\1 & \mu & -1 \\\end{matrix} \right|=0$

$\Rightarrow \mu =-39$ $\text{D}=\left| \begin{matrix}2 & 7 & \lambda \\3 & 2 & 5 \\1 & -39 & 32 \\\end{matrix} \right|=0$

$\Rightarrow \lambda =-1$ $\lambda-\mu=38$

Answer key and solution verified before publishing.

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