JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \(x+y+z=2\) \(2 x+4 y-z=6\) \(3 x+2 y+\lambda z=\mu\) has infinitely many solutions, then
- A \(\lambda-2 \mu=-5\)
- B \(2 \lambda-\mu=5\)
- C \(2 \lambda+\mu=14\)
- D \(\lambda+2 \mu=14\)
Answer & Solution
Correct Answer
(C) \(2 \lambda+\mu=14\)
Step-by-step Solution
Detailed explanation
For infinite solutions \(\Delta=\Delta_{ x }=\Delta_{ y }=\Delta_{ z }=0\) Now \(\Delta=0 \Rightarrow\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & 4 & -1 \\ 3 & 2 & \lambda\end{array}\right|=0\) \(\Rightarrow \lambda=\frac{9}{2}\)…
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