JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The set of all values of \(\lambda\) for which the system of linear \(2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}\;,\;2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}\;\;,\)\(\;\; - {x_1} + 2{x_2} = \lambda {x_3}\) has a non-trivial solution
- A contains more than two elements
- B is an empty set
- C is a singleton
- D contains two elements
Answer & Solution
Correct Answer
(D) contains two elements
Step-by-step Solution
Detailed explanation
\(2 x_{1}-2 x_{2}+x_{3}=\lambda x_{1}\) \(2 x_{1}-3 x_{2}+2 x_{3}=\lambda x_{2}\) \(-x_{1}+2 x_{2}=\lambda x_{3}\) \((2-\lambda) x_{1}-2 x_{2}+x_{3}=0\) \(2 x_{1}-(3+\lambda) x_{2}+2 x_{3}=0\) \(=-x_{1}+2 x_{2}-\lambda x_{3}=0\) \(\angle=0\)…
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