JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equation
\(\begin{aligned}
& 2 x+\lambda y+3 z=5 \\
& 3 x+2 y-z=7 \\
& 4 x+5 y+\mu z=9
\end{aligned}\)
has infinitely many solutions, then \(\left(\lambda^2+\mu^2\right)\) is equal to :
- A \(22\)
- B \(18\)
- C \(26\)
- D \(30\)
Answer & Solution
Correct Answer
(C) \(26\)
Step-by-step Solution
Detailed explanation
\(\Delta=0 \Rightarrow\left|\begin{array}{ccc}2 & \lambda & 3 \\ 3 & 2 & -1 \\ 4 & 5 & \mu\end{array}\right|=0\) \(\Rightarrow 2(2 \mu+5)+\lambda(-4-3 \mu)+3(7)=0\) \(\Rightarrow 4 \mu-3 \lambda \mu-4 \lambda+31=0\) ...(1)…
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