Row Rank and Column vectors of Matrix

For matrix $A in M_{m×n}$, let the rank be k and $r_1 , . . . , r_k$ be a subset of rows of A forming a basis of the row-space. How can we show that there exists column vectors $c_j$ such that $A =sum^k_{j=1} c_j r_j$?

I know that $c_j r_j$ is a mxn matrix and we are adding up a series of $c_j r_j$ together. But I have little idea on how to show there are column vectors $c_j$. Any help or hint is appreciated.