Is $[0,4,4]^T$ in the plane in $\mathbb{R}^3$ spanned by the columns of $A$? 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.

You should try to write $u$ as $u = Ax$ when $x$ is a 2d vector. If you can find $x$, then the answer is yes. (What is more difficult is to show that it's impossible when it is actually impossible.)
