JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(S\) be the set of all \(\lambda \in \mathrm{R}\) for which the system of linear equations \(2 x-y+2 z=2\) \(x-2 y+\lambda z=-4\) \(x+\lambda y+z=4\) has no solution. Then the set \(S\)
- A contains more than two elements.
- B is a singleton.
- C contains exactly two elements.
- D is an empty set.
Answer & Solution
Correct Answer
(C) contains exactly two elements.
Step-by-step Solution
Detailed explanation
\(2 x-y+2 z=2\) \(x-2 y+\lambda z=-4\) \(x+\lambda y+z=4\) For no solution : \(\mathrm{D}=\left|\begin{array}{ccc}2 & -1 & 2 \\ 1 & -2 & \lambda \\ 1 & \lambda & 1\end{array}\right|=0\) \(\Rightarrow 2\left(-2-\lambda^{2}\right)+1(1-\lambda)+2(\lambda+2)=0\)…
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