Suppose $f :\mathbb{R}^2 \to \mathbb{R}^3$ is the function defined by $\displaystyle{ f(x,y) = {\left[\begin{array}{c} -4x+2y\cr -2y+5x\cr 2x\cr \end{array}\right]}. }$

1. What is $f( 2, -1 )$? Enter your answer as a coordinate vector of the form <1,2,3>.
   $f( 2, -1 ) =$
2. If $f$ is a linear transformation, find the matrix $A$ such that $f(\mathbf{x}) = A \mathbf{x}$. If $f$ is not a linear transformation, enter DNE. For instance, enter [ [1,2], [3,4] ] for the matrix $\left[\begin{array}{cc} 1 &2\cr 3 &4 \end{array}\right]$.
   $A=$
3. Find bases (i.e., minimal spanning sets) for the kernel and image of $f$. Please enter your answers as comma separated lists of vectors of the form <1,2> or <1,2,3>, as appropriate.
   $\mathrm{Kernel}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
   $\mathrm{Image}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
4. The linear transformation $f$ is (select all that apply):
   A. surjective (onto)
   B. injective (one-to-one)
   C. bijective (an isomorphism)
   D. none of these