Let $$\vec{v}_1= \left[\begin{array}{c} 3\cr 4 \end{array}\right] \ \mbox{ and } \ \vec{v}_2=\left[\begin{array}{c} 1\cr 1 \end{array}\right] .$$ Let $T:{\mathbb R}^2 \rightarrow {\mathbb R}^2$ be the linear transformation satisfying $$T(\vec{v}_1)=\left[\begin{array}{c} -14\cr 2 \end{array}\right] \ \mbox{ and } \ T(\vec{v}_2)=\left[\begin{array}{c} -5\cr -1 \end{array}\right] .$$ Find the image of an arbitrary vector $\left[\begin{array}{c} x\cr y\cr \end{array}\right] .$

$T \left(\left[\begin{array}{c} x\cr y\cr \end{array}\right]\right) =$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$