Answer
$$\left. a \right) - 2{\bf{i}} + 4{\bf{j}},\,\,\,\,\,\left. b \right){\bf{i}} + {\bf{j}},\,\,\,\,\,\left. c \right)4{\bf{i}} - 7{\bf{j}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{u}} = - {\bf{i}} + 2{\bf{j}}{\text{ and }}{\bf{v}} = {\bf{i}} - {\bf{j}} \cr
& \left. a \right){\text{Find 2}}{\bf{u}} \cr
& 2{\bf{u}} = 2\left( { - {\bf{i}} + 2{\bf{j}}} \right) \cr
& 2{\bf{u}} = - 2{\bf{i}} + 4{\bf{j}} \cr
& \cr
& \left. b \right){\text{Find 2}}{\bf{u}} + 3{\bf{v}} \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = {\text{2}}\left( { - {\bf{i}} + 2{\bf{j}}} \right) + 3\left( {{\bf{i}} - {\bf{j}}} \right) \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = - 2{\bf{i}} + 4{\bf{j}} + 3{\bf{i}} - 3{\bf{j}} \cr
& {\text{2}}{\bf{u}} + 3{\bf{v}} = {\bf{i}} + {\bf{j}} \cr
& \cr
& \left. c \right){\text{Find }}{\bf{v}} - 3{\bf{u}} \cr
& {\bf{v}} - 3{\bf{u}} = {\bf{i}} - {\bf{j}} - 3\left( { - {\bf{i}} + 2{\bf{j}}} \right) \cr
& {\bf{v}} - 3{\bf{u}} = {\bf{i}} - {\bf{j}} + 3{\bf{i}} - 6{\bf{j}} \cr
& {\bf{v}} - 3{\bf{u}} = 4{\bf{i}} - 7{\bf{j}} \cr} $$
