I need to find a 2x3 matrix that does transformations from $\mathbb{R}^3$ to $\mathbb{R}^2$ given that it performs the following 3 transformations:
[![enter image description here](https://i.stack.imgur.com/m2X0M.png)](https://i.stack.imgur.com/m2X0M.png)

I know how to find 3x3 matrices by finding where $\begin{pmatrix}
1 \\
0 \\
0
\end{pmatrix}$, $\begin{pmatrix}
0 \\
1 \\
0
\end{pmatrix}$, and $\begin{pmatrix}
0 \\
0 \\
1
\end{pmatrix}$ go geometrically but for some reason I'm blanking on how to do this with something like a 2x3. What am I missing?