JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
\(S\) denote the set of all real values of \(\lambda\) such that the system of equations \(\lambda x + y + z =1\) ; \(x +\lambda y + z =1\) ; \(x + y +\lambda z =1\) is inconsistent, then \(\sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)\) is equal to
- A \(2\)
- B \(12\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{lll}\lambda & 1 & 1 \\ 1 & \lambda & 1 \\ 1 & 1 & \lambda\end{array}\right|=0\) \((\lambda+2)\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & \lambda & 1 \\ 1 & 1 & \lambda\end{array}\right|=0\)…
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