JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations
\(\begin{aligned}
& 2 x-y+z=4 \\
& 5 x+\lambda y+3 z=12 \\
& 100 x-47 y+\mu z=212
\end{aligned}\)
has infinitely many solutions, then \(\mu-2 \lambda\) is equal to
- A \(57\)
- B \(59\)
- C \(55\)
- D \(56\)
Answer & Solution
Correct Answer
(A) \(57\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & 2 x-y+z=4 \\ & 5 x+\lambda y+3 z=12 \\ & 100 x-47 y+\mu z=212 \\ & \Delta x=\Delta y=\Delta z=0 \\ & \Delta z=\left|\begin{array}{ccc}2 & -1 & 4 \\ 5 & \lambda & 12 \\ 100 & -47 & 212\end{array}\right|=0 \\ & \Rightarrow 2(212 \lambda+564)+1(1060-1200) \\ &…
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