matrices forms a basis for vector space 2x2 $\begin{bmatrix}0&1\\2&3\end{bmatrix}$
$\begin{bmatrix}3&4\\5&6\end{bmatrix}$
$\begin{bmatrix}7&8\\9&10\end{bmatrix}$
$\begin{bmatrix}11&12\\13&14\end{bmatrix}$
Show that the 4 matrix forms a basis for vector space 2x2

Hint:
Algebraically, this is the same as showing that the vectors
$$
\begin{bmatrix}0\\1\\2\\3\end{bmatrix},\ \begin{bmatrix}3\\4\\5\\6\end{bmatrix},\ \begin{bmatrix}7\\8\\9\\10\end{bmatrix},\ \begin{bmatrix}11\\12\\13\\14\end{bmatrix}
$$
(top left, top right, bottom left, bottom right) form a basis for $\mathbb{R}^4$.
(I will note, however, that as written: this is false. If the matrices are $A_1,A_2,A_3,A_4$ (respectively), then $x_1=4$, $x_2=1$, $x_3=-13$, and $x_4=8$ makes $\sum x_iA_i$ the $0$-matrix, for instance.)
