Let $u$ be the $3\times 1$ matrix $$\begin{bmatrix} 0\\ 4\\ 4 \end{bmatrix}$$
and $A$ the $3\times2$ matrix: $$\begin{bmatrix} 3 & -5\\ -2 & 6\\ 1 & 1 \end{bmatrix}.$$
Here's where the title comes in: is $u$ in the plane $\mathbb R^3$ spanned by the columns of $A$? Why or why not? I know that it is, I just don't know why. This is the chapter before we learn about linear dependence and independence, so I doubt it has to do with either of these, beyond that I haven't a clue.