1. ## Find a basis...

I have to answer the following:
Let W be the subspace of $M_{2x2}(\mathbb{R})$ consisting of the set
S=
$\{$ $\left( \begin{array}{cc}
0 & -1 \\
-1 & 1 \\
\end{array} \right) ,\left( \begin{array}{cc}
1 & 2\\
2 & 3\\
\end{array}\right) ,\left( \begin{array}{cc}
2 & 1\\
1 & 9\\
\end{array}\right) ,\left( \begin{array}{cc}
1 & -2\\
-2 & 4\\
\end{array}\right) ,\left( \begin{array}{cc}
-1 & 2\\
2 & -1\\
\end{array}\right)
$
$\}$ generates W.
Find a subset of S that is a basis for W.

I am a little lost, can someone help me with this one, or at least a hint on where to go? Thanks

2. you know that the dimension where you're working on is 4, and you have 5 vectors, so there's one there which turns those into a linear dependent set.

use coordinated vectors to express each matrix, for example the first matrix can ve expressed as $(0,-1,-1,1)$ and do the same for the others.

once done this, construct a matrix by putting the second vector below the first, then the third one below the second one and so on, finally turn that matrix in into row echelon form and the row which turns into zeros will tell you what's the vector which is bothering.

.