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________

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{D}=\mathrm{D}_1=\mathrm{D}_2=\mathrm{D}_3=0 \ & \mathrm{D}_3=\left|\begin{array}{ccc}2 & 7 & 3 \ 3 & 2 & 4 \ 1 & \mu & -1\end{array}ight|=0 \Rightarrow \mu=-39 \ & \mathrm{D}=\left|\begin{array}{ccc}2 & 7 & \lambda \ 3 & 2 & 5 \ 1 & -39 & 32\end{array}ight|=0 \Rightarrow \lambda=-1 \ & \lambda-\mu=38\end{aligned}$

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…

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