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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    Let\[A=\left[ \begin{matrix}    -1 & -2 & -2  \\    2 & 1 & -2  \\    2 & -2 & 1  \\ \end{matrix} \right]\]. If adj.  \[A=k{{A}^{T}},\] then the value of k is

    A) \[1\]                 

    B)        \[2\]

    C) \[3\]                 

    D)        \[4\]

    Correct Answer: C

    Solution :

    [c] \[|adj\,A|\,=\,|A{{|}^{2}}\] for a \[3\times 3\] matrix Given that adj \[A=k{{A}^{T}}\] \[\Rightarrow \,\,\,|adj\,A|\,=\,|k{{A}^{T}}|=\,|{{k}^{3}}|A|\] \[\therefore \,\,\,\,{{k}^{3}}|A|=\,|A{{|}^{2}}\] \[\Rightarrow \,\,\,|A|=\,{{k}^{3}}\] \[\Rightarrow \,\,\,{{k}^{3}}=27\Rightarrow k=3\]


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