> 
> What is the the rank of a $4 \times 5$ matrix whose null space is three dimensional?
> 
> 
> 

Wouldn't this mean that I would have something like

$\begin{bmatrix}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\end{bmatrix}$

So wouldn't it's rank = (the # of pivot columns) - the null space dimension? so **rank** $= 4 - 3 = 1$?