Originally Posted by

**illness** Hello, first time posting on the forum. Been here a lot in my past couple of semesters with homework help. I've browsed as much as I could for help on this problem but I haven't made any advancement. Any help would be greatly appreciated.

The problem reads

Find a basis and the dimension of the subspace W of V = $\displaystyle M_{2,2}$, spanned by

$\displaystyle A = \left(\begin{array}{cc}1&-5\\-4&2\end{array}\right)$ $\displaystyle B = \left(\begin{array}{cc}1&1\\-1&5\end{array}\right)$ $\displaystyle C = \left(\begin{array}{cc}2&-4\\-5&7\end{array}\right)$ $\displaystyle D = \left(\begin{array}{cc}1&-7\\-5&1\end{array}\right)$.

TBH I barely have any idea where to start here. I understand bases and I can do them when they involve 1x1 vectors, but these are 2x2 and have no idea how to set it up. TIA

DP