[tex]\bf f= \begin{pmatrix} -2\\ 4 \end{pmatrix}\qquad \qquad g= \begin{pmatrix} 3\\ -1 \end{pmatrix} \\\\[-0.35em] ~\dotfill\\\\ 2f\implies 2\begin{pmatrix} -2\\ 4 \end{pmatrix}\implies \begin{pmatrix} -4\\ 8 \end{pmatrix}~\hfill -4g\implies -4\begin{pmatrix} 3\\ -1 \end{pmatrix}\implies \begin{pmatrix} -12\\ 4 \end{pmatrix} \\\\[-0.35em] ~\dotfill\\\\ 2f-4g\implies 2f+(-4g)\implies \begin{pmatrix} -4\\ 8 \end{pmatrix}+ \begin{pmatrix} -12\\ 4 \end{pmatrix}\implies \begin{pmatrix} -16\\ 12 \end{pmatrix}[/tex]
