Answer
(a) $4\textbf{i}$
(b) $7\textbf{i}+3\textbf{j}$
(c) $-5\textbf{i}+\textbf{j}$
Work Step by Step
(a) To find the value of $2\textbf{u}$, we substitute the vector $\textbf{u}$ in the expression and simplify:
$2\textbf{u}=2(2\textbf{i})=4\textbf{i}$
(b) To find the value of $2\textbf{u}+3\textbf{v}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify:
$2\textbf{u}+3\textbf{v}=2(2\textbf{i})+3(\textbf{i}+\textbf{j})=4\textbf{i}+3\textbf{i}+3\textbf{j}=7\textbf{i}+3\textbf{j}$
(c) To find the value of $\textbf{v}-3\textbf{u}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify:
$\textbf{v}-3\textbf{u}=(\textbf{i}+\textbf{j})-3(2\textbf{i})=\textbf{i}+\textbf{j}-6\textbf{i}=-5\textbf{i}+\textbf{j}$
