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Math Help - Matrix Multiplication

  1. #1
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    Question Matrix Multiplication

    Find all symmetric 2x2 matrices A such that A^2 = 0.

    thank you very much.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by seit View Post
    Find all symmetric 2x2 matrices A such that A^2 = 0.

    thank you very much.
    Where are you stuck with this problem?

    There may be a more elegant solution, but I personally would just solve,

    \left( \begin{array}{cc}<br />
a & b \\<br />
c & d \\<br />
\end{array} \right)\left( \begin{array}{cc}<br />
e & f \\<br />
g & h \\<br />
\end{array} \right)=<br />
\left( \begin{array}{cc}<br />
0 & 0 \\<br />
0 & 0 \\<br />
\end{array} \right)<br />

    whilst remembering that either ad=bc or eh=gf (where did I get these from?).

    You get 4 equations in 8 unknowns, but this doesn't actually matter because all it means is that your solutions won't be unique.

    (That is, there is more than one possible solution to your equations. For example, a=b=c=d=0, all the others whatever, and a=b=c=0, d=1=e,, f=g=h=0 are two different solutions.)
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  3. #3
    Senior Member
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    Staten Island, NY
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    Thanks
    2
    You can solve this matrix equation:

    \left( \begin{array}{cc}<br />
a & b \\<br />
b & d \\<br />
\end{array} \right)\left( \begin{array}{cc}<br />
a & b \\<br />
b & d \\<br />
\end{array} \right)=<br />
\left( \begin{array}{cc}<br />
0 & 0 \\<br />
0 & 0 \\<br />
\end{array} \right)<br />
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  4. #4
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    Thanks so much. I have done this exercise.
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