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JEE Main & Advanced Mathematics Determinants & Matrices Question Bank System of linear equations, Some special determinants, differentiation and integration of determinants

  • question_answer
    The system of equations \[\lambda x+y+z=0,\] \[-x+\lambda y+z=0,\] \[-x-y+\lambda z=0\], will have a non zero solution if real values of \[\lambda \]are given by [IIT 1984]

    A) 0

    B) 1

    C) 3

    D) \[\sqrt{3}\]

    Correct Answer: A

    Solution :

    Accordingly, \[\left| \,\begin{matrix}    \lambda  & 1 & 1  \\    -1 & \lambda  & 1  \\    -1 & -1 & \lambda   \\ \end{matrix}\, \right|=0\Rightarrow {{\lambda }^{3}}+3\lambda =0\] Therefore\[\lambda =0\], since \[\lambda =i\sqrt{3}\]does not exist.


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