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J & K CET Engineering J and K - CET Engineering Solved Paper-2009

  • question_answer
    If X and Y are \[2\times 2\] matrices such that \[2X+3Y=O\] and \[X+2Y=I,\]where \[O\] and \[I\] denote the \[2\times 2\] zero matrix and the \[2\times 2\] identity matrix, then X is equal to

    A)  \[\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right]\]

    B)  \[\left[ \begin{matrix}    2 & 0  \\    0 & 2  \\ \end{matrix} \right]\]

    C)  \[\left[ \begin{matrix}    -3 & 0  \\    0 & -3  \\ \end{matrix} \right]\]

    D)  \[\left[ \begin{matrix}    3 & 0  \\    0 & 3  \\ \end{matrix} \right]\]

    Correct Answer: C

    Solution :

    Given, \[2X+3Y=O\] .....(i) and \[X+2Y=I\] ??(ii) Where \[O=\left[ \begin{matrix}    0 & 0  \\    0 & 0  \\ \end{matrix} \right]\] and \[I=\left[ \begin{matrix}    1 & 0  \\    0 & 1  \\ \end{matrix} \right]\] On solving Eqs. (i) and (ii), we get \[X=-3I=\left[ \begin{matrix}    -3 & 0  \\    0 & -3  \\ \end{matrix} \right]\]


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