For some vectors $v_1, v_2$ and a matrix $A$, I currently have that $v_1 A = v_2$. I want a representation that has $A$ on the left of $v_1$, but $A$ can be modified. I'm looking for some $A'$ such that $A' v_1 = v_2$.
What modifications do I have to make to $A$ to get such a representation?