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JEE Main & Advanced Sample Paper JEE Main Sample Paper-43

  • question_answer
    The set of all \[2\times 2\] matrices which commute with the matrix with respect to matrix\[\left[ \begin{matrix}    1 & 1  \\    1 & 0  \\ \end{matrix} \right]\]multiplication is

    A)  \[\left\{ \left[ \begin{matrix}    a & b  \\    c & a-b  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]

    B)  \[\left\{ \left[ \begin{matrix}    a & b  \\    b & c  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]

    C) \[\left\{ \left[ \begin{matrix}    a-b & b  \\    b & c  \\ \end{matrix} \right];\,\,a,\,\,b,\,\,c\,\,\in \,R \right\}\]

    D)  \[\left\{ \left[ \begin{matrix}    a & b  \\    b & a-b  \\ \end{matrix} \right];\,\,a,\,\,b\,\,\in \,R \right\}\]

    Correct Answer: D

    Solution :

     Let the matrix be \[\omega =\frac{3v}{4l}\] \[T=2\pi \,\sqrt{\frac{L}{g}}\] \[\frac{L}{2}\] \[\Rightarrow \] \[T=2\pi \sqrt{\frac{L}{2g}}\]           \[\Rightarrow \] \[M=(AL)d\,\,\,\Rightarrow \,\,\frac{M}{Ad}\]            \[\Rightarrow \] Set of all matrices that commute with \[T=2\pi \,\,\sqrt{\frac{M}{2Adg}}\] w.r.t. Matrix multiplication \[\Delta DBS,\]


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