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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2005

  • question_answer
    If \[A=\left[ \begin{matrix}    1 & -1 & 1  \\    0 & 2 & -3  \\    2 & 1 & 0  \\ \end{matrix} \right]\]and\[B=(adj\text{ }A),\]and \[C=5A,\]then \[\frac{|adj\,B|}{|C|}\]is equal to:

    A)  5                                            

    B)  25

    C)  \[-1\]                   

    D)         1

    E)  125

    Correct Answer: D

    Solution :

    \[\because \] \[a=\left[ \begin{matrix}    1 & -1 & 1  \\    0 & 2 & -3  \\    2 & 1 & 0  \\ \end{matrix} \right]\] \[\therefore \] \[B=adjA=\left[ \begin{matrix}    3 & 1 & 1  \\    -6 & -2 & 3  \\    -4 & -3 & 2  \\ \end{matrix} \right]\] Therefore adj \[B=\left[ \begin{matrix}    5 & -5 & 5  \\    0 & 10 & -15  \\    10 & 5 & 0  \\ \end{matrix} \right]\] Now\[|adj\,B|=\left| \begin{matrix}    5 & -5 & 5  \\    0 & 10 & -15  \\    10 & 5 & 0  \\ \end{matrix} \right|=625\] and| \[|C|=125|A|=125\left| \begin{matrix}    1 & -1 & 1  \\    0 & 2 & -3  \\    2 & 1 & 0  \\ \end{matrix} \right|=625\] \[\therefore \]  \[\frac{|adj\,B|}{|C|}=\frac{625}{625}=1\]


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