This might be a dumb question, it's been a long time since I've done any linear algebra.
I have an $M_{m\times n}$ matrix, who's values are the sum of a row and column vectors $\vec{x}_{1\times n}$ and $\vec{y}_{m\times 1}$. eg:
$M=\begin{bmatrix} x_1+y_1&x_2+y_1 &\cdots& x_n+y_1 \\ x_1+y_2&x_2+y_2 &\cdots& x_n+y_2 \\ \vdots & \vdots & \ddots & \vdots \\ x_1+y_m & x_2+y_m & \cdots & x_n+y_m \end{bmatrix}$
If I know the values of $M$, how do I solve for $x$ and $y$?
I'm sure there's a name for this, but I can't remember.