JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \( 11 x+y+\lambda z=-5 \) \( 2 x+3 y+5 z=3 \) \( 8 x-19 y-39 z=\mu\) has infinitely many solutions, then \(\lambda^4-\mu\) is equal to :
- A \(49\)
- B \(45\)
- C \(47\)
- D \(51\)
Answer & Solution
Correct Answer
(C) \(47\)
Step-by-step Solution
Detailed explanation
\( 11 x+y+\lambda z=-5 \) \( 2 x+3 y+5 z=3 \) \( 8 x-19 y-39 z=\mu\) for infinite sol. \(\mathrm{D}=\left|\begin{array}{ccc}11 & 1 & \lambda \\ 2 & 3 & 5 \\ 8 & -19 & -39\end{array}\right|=0\) \( \Rightarrow 11(-117+95)-1(-78-40)+\lambda(-38-24) \)…
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