Answer
$$\eqalign{
& \left( {\bf{a}} \right){\bf{i}} \cr
& \left( {\bf{b}} \right)4{\bf{i}} - 2{\bf{j}} \cr
& \left( {\bf{c}} \right)11{\bf{i}} - 7{\bf{j}} \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Let }}{\bf{v}} = 2{\bf{i}} - {\bf{j}}{\text{ and }}{\bf{u}} = - 3{\bf{i}} + 2{\bf{j}} \cr
& \cr
& \left( {\bf{a}} \right){\text{ 2}}{\bf{v}}{\text{ + }}{\bf{u}} \cr
& {\text{ 2}}{\bf{v}}{\text{ + }}{\bf{u}} = 2\left( {2{\bf{i}} - {\bf{j}}} \right) + \left( { - 3{\bf{i}} + 2{\bf{j}}} \right) \cr
& {\text{Simplify}} \cr
& {\text{ 2}}{\bf{v}}{\text{ + }}{\bf{u}} = 4{\bf{i}} - 2{\bf{j}} - 3{\bf{i}} + 2{\bf{j}} \cr
& {\text{ 2}}{\bf{v}}{\text{ + }}{\bf{u}} = {\bf{i}} \cr
& \cr
& \left( {\bf{b}} \right){\text{ 2}}{\bf{v}} \cr
& {\text{ 2}}{\bf{v}} = 2\left( {2{\bf{i}} - {\bf{j}}} \right) \cr
& {\text{Simplify}} \cr
& {\text{ 2}}{\bf{v}} = 4{\bf{i}} - 2{\bf{j}} \cr
& \cr
& \left( {\bf{c}} \right){\text{ }}{\bf{v}} - 3{\bf{u}} \cr
& {\text{ }}{\bf{v}} - 3{\bf{u}} = \left( {2{\bf{i}} - {\bf{j}}} \right) - 3\left( { - 3{\bf{i}} + 2{\bf{j}}} \right) \cr
& {\text{Simplify}} \cr
& {\text{ }}{\bf{v}} - 3{\bf{u}} = 2{\bf{i}} - {\bf{j}} + 9{\bf{i}} - 6{\bf{j}} \cr
& {\text{ }}{\bf{v}} - 3{\bf{u}} = 11{\bf{i}} - 7{\bf{j}} \cr} $$
