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Thread: Matrices.

  1. #1
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    Matrices.

    (Sorry, posting a lot of threads tonight. Exams coming up, past papers are surprisingly unlike my notes )

    A = $\displaystyle \begin{pmatrix}0&1\\1&0\end{pmatrix}$

    Determine all 2 x 2 matrices B such that AB-BA = $\displaystyle \begin{pmatrix}1&0\\0&-1\end{pmatrix}$

    I really don't know how to even start this one. Could anybody give any pointers?





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  2. #2
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    Let $\displaystyle B = \left( {\begin{array}{*{20}c}
    w & x \\ y & z \\ \end{array} } \right)$
    Find $\displaystyle w,~x,~y,~\&~z$ so that $\displaystyle AB - BA = \left( {\begin{array}{*{20}c} 1 & 0 \\ 0 & { - 1} \\
    \end{array} } \right)$
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  3. #3
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    Quote Originally Posted by Plato View Post
    Let $\displaystyle B = \left( {\begin{array}{*{20}c}
    w & x \\ y & z \\ \end{array} } \right)$
    Find $\displaystyle w,~x,~y,~\&~z$ so that $\displaystyle AB - BA = \left( {\begin{array}{*{20}c} 1 & 0 \\ 0 & { - 1} \\
    \end{array} } \right)$
    Ok, so I've tried to work though it that way but I've hit a snag. Perhaps I've multiplied wrongly? Can you see the error?

    $\displaystyle AB = \left( {\begin{array}{*{20}c}
    z & y \\ w & x \\ \end{array} } \right)$

    $\displaystyle BA = \left( {\begin{array}{*{20}c}
    z & y \\ x & w \\ \end{array} } \right)$

    So, AB - BA :

    $\displaystyle B = \left( {\begin{array}{*{20}c}
    y-z & z-y \\ w-x & x-w \\ \end{array} } \right)$

    Which leaves the situation of y always having to be one bigger than z, but z always having to equal y, which can't be true?
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  4. #4
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    If you have any hope of passing this test then you better improve basic skills.
    $\displaystyle BA = \left( {\begin{array}{*{20}c}
    x & w \\
    z & y \\

    \end{array} } \right)
    $
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