Here is my problem:
I have a sytem consisting of $2 \times 2$ matrices and I do not know what method to use to solve it.
Here is the system (excuse me for the clumsy notation) \begin{equation} \begin{bmatrix} 1 & 0 \\ 0 & 2\end{bmatrix} u + \begin{bmatrix}3 & -3 \\ -1 & -1 \end{bmatrix} v = \begin{bmatrix} 1 \\ 4 \end{bmatrix} \end{equation} and \begin{equation} \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} u + \begin{bmatrix} 1 & 0 \\1 & -1\end{bmatrix} v= \begin{bmatrix} 0 \\ -2 \end{bmatrix} \end{equation}
What I thought of is to use inverses and come to $u+v = a$ matrix.
Is that right?
Thanks for the help