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