Say $A \in \mathbb{R}_+^{m \times n}$ and $B \in \mathbb{R}_+^{m \times m}$. Let $X \in \mathbb{R}^{n \times m}$ denote the matrix of unknowns.
Suppose $A ~\&~ B$ are (non-negative) row-stochastic matrices, i.e, $\sum_j A_{ij} = 1$ and $\sum_j B_{ij} = 1$ for all $i \in \{1,2, \cdots,m\}$.
When can one find solutions to $AX = B$ or the matrix $X$ such that $X$ is (non-negative) row stochastic.? Is this always the case?
Here by non-negative I mean each entry is non-negative.
Any pointers would be appreciated.