Let $V$ be a vector space and let $\vec{v}_1, \vec{v}_2, \vec{v}_3 \in V$. Suppose $f : V \to \mathbb{R}^{3}$ is a linear transformation and $$f(\vec{v}_1) = \left( \begin{array}{r} -3 \\ 3 \\ 2 \end{array} \right), \ \ \ f(\vec{v}_2) = \left( \begin{array}{r} 1 \\ 5 \\ -1 \end{array} \right), \ \ \ f(\vec{v}_3) = \left( \begin{array}{r} -3 \\ -3 \\ 1 \end{array} \right).$$

1. Find $f( 3 \vec{v}_1 + 6 \vec{v}_2 - 4 \vec{v}_3)$.
   
   $f( 3 \vec{v}_1 + 6 \vec{v}_2 - 4 \vec{v}_3) =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.
   
   
2. If $V$ has dimension $3$ and $\lbrace \vec{v}_1, \vec{v}_2, \vec{v}_3 \rbrace$ is a linearly independent set, then the linear transformation $f$ is
   injective
   surjective
   an isomorphism
   none of these