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

  • question_answer
    If \[2X-\left[ \begin{matrix}    1 & 2  \\    7 & 4  \\ \end{matrix} \right]=\left[ \begin{matrix}    3 & 2  \\    0 & -2  \\ \end{matrix} \right]\], then X is equal to   [RPET 2001]

    A) \[\left[ \begin{matrix}    2 & 2  \\    7 & 4  \\ \end{matrix} \right]\]

    B) \[\left[ \begin{matrix}    1 & 2  \\    7/2 & 2  \\ \end{matrix} \right]\]

    C) \[\left[ \begin{matrix}    2 & 2  \\    7/2 & 1  \\ \end{matrix} \right]\]

    D) None of these

    Correct Answer: C

    Solution :

    \[2X-\left[ \begin{matrix}    1 & 2  \\    7 & 4  \\ \end{matrix} \right]\,=\,\left[ \begin{matrix}    3 & 2  \\    0 & -2  \\ \end{matrix} \right]\] Þ \[2X=\left[ \begin{matrix}    3 & 2  \\    0 & -2  \\ \end{matrix} \right]+\left[ \begin{matrix}    1 & 2  \\    7 & 4  \\ \end{matrix} \right]\] Þ \[2X=\left[ \begin{matrix}    4 & 4  \\    7 & 2  \\ \end{matrix} \right]\] Þ \[X=\left[ \begin{matrix}    2 & 2  \\    7/2 & 1  \\ \end{matrix} \right]\].


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