Let $f : \mathbb{R}^{3} \to \mathbb{R}^{2}$ be the linear transformation determined by $f(\vec{x}) = A \vec{x}$ where $$A=\left[\begin{array}{ccc} -3 &2 &-1\cr 5 &-1 &4 \end{array}\right]$$

1. Find a formula for $f(\vec{x})$.
   
   $\displaystyle f \left( \begin{array}{c} x \\ y \\ z \end{array} \right) =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$
   
   
2. Find bases (i.e., minimal spanning sets) for the kernel and image of $f$. vector
   $\mathrm{Kernel}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
   $\mathrm{Image}(f) = \mathrm{span} \Big\lbrace$ $\Big\rbrace.$
   
   
3. The linear transformation $f$ is
   injective
   surjective
   bijective
   none of these