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

thank you very much.

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- Jan 12th 2011, 12:44 AMseitMatrix Multiplication
Find all symmetric 2x2 matrices A such that A^2 = 0.

thank you very much. - Jan 12th 2011, 01:02 AMSwlabr
Where are you stuck with this problem?

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

$\displaystyle \left( \begin{array}{cc}

a & b \\

c & d \\

\end{array} \right)\left( \begin{array}{cc}

e & f \\

g & h \\

\end{array} \right)=

\left( \begin{array}{cc}

0 & 0 \\

0 & 0 \\

\end{array} \right)

$

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.) - Jan 12th 2011, 03:17 AMDrSteve
You can solve this matrix equation:

$\displaystyle \left( \begin{array}{cc}

a & b \\

b & d \\

\end{array} \right)\left( \begin{array}{cc}

a & b \\

b & d \\

\end{array} \right)=

\left( \begin{array}{cc}

0 & 0 \\

0 & 0 \\

\end{array} \right)

$ - Jan 12th 2011, 03:39 AMseit
Thanks so much. I have done this exercise.