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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 35

  • question_answer
    Let \[A=[{{a}_{ij}}]\] be a matrix of order \[3\times 3\] and \[B=[{{b}_{ij}}]\] be another matrix of order \[3\times 3\] such that \[{{b}_{ij}}\] is the sum of the elements of \[{{i}^{th}}\] row of A except\[{{a}_{ij}}\]. If det. \[(A)=3,\] then the value of det. \[(B)\] is equal to

    A) \[2\]                      

    B)        \[4\]                     

    C) \[6\]        

    D)        \[8\]

    Correct Answer: C

    Solution :

    [c] \[A=\left[ \begin{matrix}    {{a}_{11}} & {{a}_{12}} & {{a}_{13}}  \\    {{a}_{21}} & {{a}_{22}} & {{a}_{23}}  \\    {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right]\]  and  \[|A|=3\] According to the question, \[B=\left[ \begin{matrix}    {{a}_{12}}+{{a}_{13}} & {{a}_{11}}+{{a}_{13}} & {{a}_{11}}+{{a}_{12}}  \\    {{a}_{22}}+{{a}_{23}} & {{a}_{21}}+{{a}_{23}} & {{a}_{21}}+{{a}_{22}}  \\    {{a}_{32}}+{{a}_{33}} & {{a}_{31}}+{{a}_{33}} & {{a}_{31}}+{{a}_{32}}  \\ \end{matrix} \right]\] \[\Rightarrow \,\,|B|\,\,=\,\,\left| \begin{matrix}    {{a}_{11}} & {{a}_{12}} & {{a}_{13}}  \\    {{a}_{21}} & {{a}_{22}} & {{a}_{23}}  \\    {{a}_{31}} & {{a}_{32}} & {{a}_{33}}  \\ \end{matrix} \right|\,\,\left| \begin{matrix}    0 & 1 & 1  \\    1 & 0 & 1  \\    1 & 1 & 0  \\ \end{matrix} \right|=3\times 2=6\]           


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