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

  • question_answer
    The existence of the unique solution of the system \[x+y+z=\lambda ,\] \[5x-y+\mu z=10\], \[2x+3y-z=6\] depends on [Kurukshetra CEE 2002]

    A) \[\mu \]only

    B) \[\lambda \]only

    C) \[\lambda \]and \[\mu \] both

    D) Neither \[\lambda \]nor \[\mu \]

    Correct Answer: A

    Solution :

    For unique solution of the given system \[D\ne 0\] \[\left| \,\begin{matrix}    1 & 1 & 1  \\    5 & -1 & \mu   \\    2 & 3 & -1  \\ \end{matrix}\, \right|\ne 0\]. So this depends on \[\mu \] only.


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