The figure below shows where a linear transformation $f$ maps the three standard basis vectors from its domain. The grids in the figures are unit grids. Vectors with their tip on the grid are in the $xy$-plane, while vectors with their tip not on integer-coordinate points the grid are not in the $xy$-plane.
1. $f : \mathbb{R}^k \to \mathbb{R}^n$ for $k=$ and $n=$ .
2. The set of vectors $\lbrace \, \mathbf{e_1}, \mathbf{e_2}, \mathbf{e_3} \rbrace \,$ is (select all that apply):

3. The set of vectors $\lbrace \, f(\mathbf{e_1}), \, f(\mathbf{e_2}), \, f(\mathbf{e_3}) \, \rbrace$ is (select all that apply):

4. The linear transformation $f$ is (select all that apply):

5. Find the matrix for the linear transformation $f$ (relative to the standard basis in the domain and codomain). That is, find the matrix $A$ such that $f(\mathbf{x}) = A \mathbf{x}$. For instance, enter [ [1,2], [3,4] ] for the matrix ${\left[\begin{array}{cc} 1 &2\cr 3 &4 \end{array}\right]}$.
$A=$

In order to get credit for this problem all answers must be correct.