Search any question & find its solution
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________
$\begin{aligned}
& 2 x+7 y+\lambda z=3 \\
& 3 x+2 y+5 z=4 \\
& x+\mu y+32 z=-1
\end{aligned}$
has infinitely many solutions, then $(\lambda-\mu)$ is equal to________
Solution:
2320 Upvotes
Verified Answer
The correct answer is:
38
$\begin{aligned} & \mathrm{D}=\mathrm{D}_1=\mathrm{D}_2=\mathrm{D}_3=0 \\ & \mathrm{D}_3=\left|\begin{array}{ccc}2 & 7 & 3 \\ 3 & 2 & 4 \\ 1 & \mu & -1\end{array}\right|=0 \Rightarrow \mu=-39 \\ & \mathrm{D}=\left|\begin{array}{ccc}2 & 7 & \lambda \\ 3 & 2 & 5 \\ 1 & -39 & 32\end{array}\right|=0 \Rightarrow \lambda=-1 \\ & \lambda-\mu=38\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.