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Math Help - 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 =  \begin{pmatrix}0&1\\1&0\end{pmatrix}

    Determine all 2 x 2 matrices B such that AB-BA =  \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 B = \left( {\begin{array}{*{20}c}<br />
   w & x  \\   y & z  \\ \end{array} } \right)
    Find w,~x,~y,~\&~z so that AB - BA = \left( {\begin{array}{*{20}c}   1 & 0  \\   0 & { - 1}  \\<br />
 \end{array} } \right)
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  3. #3
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    Quote Originally Posted by Plato View Post
    Let B = \left( {\begin{array}{*{20}c}<br />
   w & x  \\   y & z  \\ \end{array} } \right)
    Find w,~x,~y,~\&~z so that AB - BA = \left( {\begin{array}{*{20}c}   1 & 0  \\   0 & { - 1}  \\<br />
 \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?

    AB = \left( {\begin{array}{*{20}c}<br />
   z & y \\ w & x  \\ \end{array} } \right)

    BA = \left( {\begin{array}{*{20}c}<br />
   z & y  \\ x & w  \\ \end{array} } \right)

    So, AB - BA :

    B = \left( {\begin{array}{*{20}c}<br />
   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.
    BA = \left( {\begin{array}{*{20}c}<br />
   x & w  \\<br />
   z & y  \\<br /> <br />
 \end{array} } \right)<br />
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