JEE Main & Advanced Mathematics Determinants & Matrices Question Bank Types of matrices, Algebra of matrices

  • question_answer
    \[\left[ \begin{matrix}    7 & 1 & 2  \\    9 & 2 & 1  \\ \end{matrix} \right]\left[ \begin{matrix}    3  \\    4  \\    5  \\ \end{matrix} \right]+2\left[ \begin{matrix}    4  \\    2  \\ \end{matrix} \right]\]  is equal to [DCE 2002]

    A) \[\left[ \begin{align}   & 43 \\  & 44 \\ \end{align} \right]\]

    B) \[\left[ \begin{align}   & 43 \\  & 45 \\ \end{align} \right]\]

    C) \[\left[ \begin{align}   & 45 \\  & 44 \\ \end{align} \right]\]

    D) \[\left[ \begin{align}   & 44 \\  & 45 \\ \end{align} \right]\]

    Correct Answer: A

    Solution :

    \[\left[ \begin{matrix}    7 & 1 & 2  \\    9 & 2 & 1  \\ \end{matrix} \right]\,\left[ \begin{matrix}    3  \\    4  \\    5  \\ \end{matrix} \right]\,=\,\,\left[ \begin{matrix}    35  \\    40  \\ \end{matrix} \right]\]; \ \[\left[ \begin{matrix}    35  \\    40  \\ \end{matrix} \right]\,+\,\left[ \begin{matrix}    8  \\    4  \\ \end{matrix} \right]\,=\,\left[ \begin{matrix}    43  \\    44  \\ \end{matrix} \right]\].


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