Find row and column vectors given a matrix of sums.

Question

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.

Answer 1

I don't think this is solvable in all honesty.