Finding a basis

**amm345** · Oct 27th 2009, 08:09 PM

Find a basis for Mmxn(F).

I'm not sure how to approach this question, any help would be great.

**HallsofIvy** · Oct 28th 2009, 05:43 AM

Starting with the definition of basis woud be good!

Also, notice that
$\begin{bmatrix}a & b \\ c & d \end{bmatrix}= \begin{bmatrix}a & 0 \\ 0 & 0 \end{bmatrix}+ \begin{bmatrix}0 & b \\ 0 & 0\end{bmatrix}+ \begin{bmatrix}0 & 0 \\ c & 0\end{bmatrix}+ \begin{bmatrix}0 & 0 \\ 0 & d\end{bmatrix}$

$= a\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}+ b\begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix}+ c\begin{bmatrix}0 & 0 \\ 1 & 0\end{bmatrix}+ d\begin{bmatrix}0 & 0 \\ 0 & 1\end{bmatrix}$

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