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VIT Engineering VIT Engineering Solved Paper-2007

  • question_answer
    If the rank of the matrix \[\left| \begin{matrix}  -1 & 2 & 5  \\    2 & -4 & a-4  \\    1 & -2 & a+1  \\ \end{matrix} \right|\] is 1 then the value of a is :

    A)  \[-1\]

    B)  \[2\]

    C)  \[-6\]

    D)  \[4\]

    Correct Answer: C

    Solution :

    Since, the rank of matrix \[\left[ \begin{matrix}    -1 & 2 & 5  \\    2 & -4 & a-4  \\    1 & -2 & a+1  \\ \end{matrix} \right]\]is 1, then \[\left| \begin{matrix}    2 & 5  \\    -4 & a-4  \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[2a-8+20=0\] \[\Rightarrow \]        \[2a+12=0\] \[\Rightarrow \]    \[a=-\,6\]


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