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JEE Main & Advanced JEE Main Paper (Held on 12-4-2019 Morning)

  • question_answer
    If a is A symmetric matrix and B is a skewsymmetrix matrix such that \[A+B=\left[ \begin{matrix}    2 & 3  \\ 5 & -1  \\ \end{matrix} \right],\]then AB is equal to :                              [JEE Main Held on 12-4-2019 Morning]

    A) \[\left[ \begin{matrix}    -4 & 2  \\    1 & 4  \\ \end{matrix} \right]\]  

    B) \[\left[ \begin{matrix}    -4 & -2  \\    -1 & 4  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    4 & -2  \\    -1 & -4  \\ \end{matrix} \right]\]

    D) \[\left[ \begin{matrix}    4 & -2  \\    1 & -4  \\ \end{matrix} \right]\]

    Correct Answer: C

    Solution :

    \[A=A',B=B'\] \[A+B=\left[ \begin{matrix}    2 & 3  \\    5 & -1  \\ \end{matrix} \right]\]                           ...(1) \[A'+B'=\left[ \begin{matrix}    2 & 5  \\    3 & -1  \\ \end{matrix} \right]\] \[A-B=\left[ \begin{matrix}    2 & 5  \\    3 & -1  \\ \end{matrix} \right]\]                           ...(2) After adding Eq. (1) & (2) \[A=\left[ \begin{matrix}    2 & 4  \\    4 & -1  \\ \end{matrix} \right],B=\left[ \begin{matrix}    0 & -1  \\    1 & 0  \\ \end{matrix} \right]\] \[AB=\left[ \begin{matrix}    4 & -2  \\    -1 & -4  \\ \end{matrix} \right]\]              


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