This is an exercise and it is divided into steps. The first step says:
Suppose $A\in\mathbb{R}^{m\times n}$ has rank 1. Let $u_1\in\mathbb{R}^m$ be a vector in $R(A)$ such that $\left \| u_1 \right \|_2=1$. Show that every column of $A$ is a multiple of $u_1$. Show that $A$ can be written in the form $A=\sigma_1u_1v_1^T$, where $v_1\in\mathbb{R}^m, \left \| v_1 \right \|_2=1$, and $\sigma_1>0$.
I'm getting confused because I keep wanting to use properties of SVD and I know I can't. I'm hoping a hint will put me on track.