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JEE Main & Advanced JEE Main Solved Paper-2015

  • question_answer
    The set of all values of \[\lambda \]for which the system of linear equations: \[2{{x}_{1}}-2{{x}_{2}}+{{x}_{3}}=\lambda {{x}_{1}}\] \[2{{x}_{1}}-3{{x}_{2}}+2{{x}_{3}}=\lambda {{x}_{2}}\] \[-{{x}_{1}}+2{{x}_{2}}=\lambda {{x}_{3}}\]has a non- trivial solution, [JEE Main Solved Paper-2015 ]

    A) Contains two elements

    B) Contains more than two elements.

    C) Is an empty set                

    D) Is a singleton.

    Correct Answer: A

    Solution :

    To have Non- Trivial solution \[D=0\Rightarrow \left| \begin{matrix}    \lambda -2 & 2 & -1  \\    2 & -3-\lambda  & 2  \\    -1 & 2 & -\lambda   \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[{{\lambda }^{3}}+{{\lambda }^{2}}-5\lambda +3=0\] \[\lambda =1,1,3\] Hence\[\lambda \] have 2 Values


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