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Manipal Engineering Manipal Engineering Solved Paper-2011

  • 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

    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,\[\Delta \ne 0\] i.e.,                        \[\left| \begin{matrix}    1 & 1 & 1  \\    5 & -1 & \mu   \\    2 & 3 & -1  \\ \end{matrix} \right|\ne 0\] Hence, it depends only on \[\mu \].


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