Answer
$$\left. a \right)\left\langle { - 2,4} \right\rangle ,\,\,\,\,\,\left. b \right)\left\langle { - 17,2} \right\rangle ,\,\,\,\,\,\left. c \right)\left\langle {9,5} \right\rangle $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = \left\langle { - 2, - 1} \right\rangle {\text{ and }}{\bf{v}} = \left\langle { - 3,2} \right\rangle \cr
& \left. a \right){\text{Find 2}}{\bf{u}} \cr
& 2{\bf{u}} = 2\left\langle { - 2, - 1} \right\rangle \cr
& 2{\bf{u}} = \left\langle { - 4, - 2} \right\rangle \cr
& \cr
& \left. b \right){\text{Find 2}}{\bf{u}} + 3{\bf{v}} \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = {\text{2}}\left\langle { - 4, - 2} \right\rangle + 3\left\langle { - 3,2} \right\rangle \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = \left\langle { - 8, - 4} \right\rangle + \left\langle { - 9,6} \right\rangle \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = \left\langle { - 8 - 9, - 4 + 6} \right\rangle \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = \left\langle { - 17,2} \right\rangle \cr
& \cr
& \left. c \right){\text{Find }}{\bf{v}} - 3{\bf{u}} \cr
& {\bf{v}} - 3{\bf{u}} = \left\langle { - 3,2} \right\rangle - 3\left\langle { - 2, - 1} \right\rangle \cr
& {\bf{v}} - 3{\bf{u}} = \left\langle { - 3,2} \right\rangle + \left\langle {6,3} \right\rangle \cr
& {\bf{v}} - 3{\bf{u}} = \left\langle {3 + 6,2 + 3} \right\rangle \cr
& {\bf{v}} - 3{\bf{u}} = \left\langle {9,5} \right\rangle \cr} $$
