Answer
(a) $\langle -4,-8 \rangle$
(b) $\langle 12,0 \rangle$
(c) $\langle -4,4 \rangle$
Work Step by Step
First, we find the vector notations of both $\textbf{u}$ and $\textbf{v}$. Upon observation, we find that $\textbf{u}=\langle 4,-4 \rangle$ and $\textbf{v}=\langle -8,-4 \rangle$.
(a) To find the value of $\textbf{u}+\textbf{v}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify:
$\textbf{u}+\textbf{v}$
$=\langle 4,-4 \rangle+\langle -8,-4 \rangle$
$=\langle 4-8,-4-4\rangle$
$=\langle -4,-8 \rangle$
(b) To find the value of $\textbf{u}-\textbf{v}$, we substitute the vectors $\textbf{u}$ and $\textbf{v}$ in the expression and simplify:
$\textbf{u}-\textbf{v}$
$=\langle 4,-4 \rangle-\langle -8,-4 \rangle$
$=\langle 4-(-8),-4-(-4)\rangle$
$=\langle 4+8,-4+4\rangle$
$=\langle 12,0 \rangle$
(c) To find the value of $-\textbf{u}$, we substitute the vector $\textbf{u}$ in the expression and simplify:
$-\textbf{u}$
$=-\langle 4,-4 \rangle$
$=\langle -1(4),-1(-4) \rangle$
$=\langle -4,4 \rangle$
