Let $f : \mathbb{R}^{2} \to \mathbb{R}^{3}$ be the linear transformation determined by $$f(\vec{e}_1) = \left( \begin{array}{r} -15 \\ 5 \\ -15 \end{array} \right), \ \ \ \ \ f(\vec{e}_2) = \left( \begin{array}{r} -6 \\ 2 \\ -6 \end{array} \right).$$

1. Find $\displaystyle f \left( \begin{array}{c} 2 \\ -1 \end{array} \right)$.
   
   $\displaystyle f \left( \begin{array}{c} 2 \\ -1 \end{array} \right) =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.
   
   
2. Find the matrix of the linear transformation $f$.
   
   $\displaystyle f \left( \begin{array}{c} x \\ y \end{array} \right) =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$ $\displaystyle \left\lbrack \begin{array}{c} x \\ y \end{array} \right\rbrack.$
   
   
3. The linear transformation $f$ is
   injective
   surjective
   bijective
   none of these