A rank one matrix can be written in a special form Any rank one matrix can be written in the form $uv^{t}$, where $u,v$ are column vectors considered as matrices and $t$ denotes transposition. 
Why? How?

Hint: Here's a rank-1 matrix:
$$
\begin{bmatrix}
1 & 2 & 5 \\
2 & 4 & 10 \\
4 & 8 & 20 \\
5 & 10 & 25
\end{bmatrix}.
$$
Look closely at the columns and see if you notice anything about them. Then try to write this matrix in the form $u v^t$. Sub-hint: use the first column as $u$. What size will $v$ be? 
Then generalize. 
