Checking linear combinations of $2 \times 2$ matrices What method would I use to verify that this matrix:
$
\begin{bmatrix}
6 & -8 \\
-1 & -8 \\
\end{bmatrix}
$
is a linear combination of these three matrices
$A = \begin{bmatrix}
4 & 0 \\
-2 & -2 \\
\end{bmatrix}
$  
$
B = \begin{bmatrix}
1 & -1 \\
2 & 3 \\
\end{bmatrix}
$
$
C = \begin{bmatrix}
0 & 2 \\
1 & 4 \\
\end{bmatrix}
$  
Would I just turn these matrices into four element column vectors and do Gaussian elimination? or is there a more appropriate method for this?

It is exactly the same problem as showing that the vector $[6,−8,−1,−8]$ is a linear combination of the vectors $[4,0,−2,−2]$, $[1,−1,2,3]$, $[0,2,1,4]$. So yes, Gaussian elimination is what you want. 
