I have a system of linear equations that I can't solve. I need help. If anyone can help, I'll appreciate. Thanks a lot.
$$ \left\{ \begin{array}{c} Ax+By=C \\ Dx+Ey=F \\ \end{array} \right. $$
where $A,B,D,E$ are square matrices and $x,y,C,F$ are column vectors. They are not a constant, so I got stuck here.
Let's say we have $n\times n$ matrices $A,B,D,E$ and $n\times 1$ matrices $x,y,C,F$. Set up a system $$Gz=H,$$ using the block matrices $$G=\begin{pmatrix} A & B \\ D & E \end{pmatrix}, \qquad z=\begin{pmatrix} x \\ y \end{pmatrix}, \qquad H=\begin{pmatrix} C \\ E \end{pmatrix}. $$ Solve this system for $z$, then you will have obtained the components of $x$ and $y$.