JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The set of all values of \(\lambda \) for which the system of linear equations \(x - 2y - 2z = \lambda x\) ; \(x + 2y + z = \lambda y\) ; \(-x - y = \lambda z\) has non zero solutions.
- A is a singleton
- B contains exactly two elements
- C is an empty set
- D contains more than two elements
Answer & Solution
Correct Answer
(A) is a singleton
Step-by-step Solution
Detailed explanation
\(\left| {\begin{array}{*{20}{c}} {\lambda - 1}&2&2\\ 1&{2 - \lambda }&1\\ 1&1&1 \end{array}} \right| = 0\) \( \Rightarrow {\left( {\lambda - 1} \right)^3} = 0 \Rightarrow \lambda = 1\)
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