Answer
$$u=\begin{bmatrix}
-1 \\
2\\
\end{bmatrix}
,
v=\begin{bmatrix}
-3 \\
-1\\
\end{bmatrix}
,
-v=\begin{bmatrix}
3 \\
1\\
\end{bmatrix},
-2v=\begin{bmatrix}
6 \\
2\\
\end{bmatrix}, $$$$
u+v=\begin{bmatrix}
-4 \\
1\\
\end{bmatrix}, u-v=\begin{bmatrix}
2 \\
3\\
\end{bmatrix},
u-2v=\begin{bmatrix}
5 \\
4\\
\end{bmatrix}
$$
Work Step by Step
Addition and subtraction operations are carried out by adding or subtracting corresponding entries in the matrix, while scalar multiplication distributes the scalar to each entry in the matrix:
$$u=\begin{bmatrix}
-1 \\
2\\
\end{bmatrix}
,
v=\begin{bmatrix}
-3 \\
-1\\
\end{bmatrix}
,
-v=\begin{bmatrix}
3 \\
1\\
\end{bmatrix},
-2v=\begin{bmatrix}
6 \\
2\\
\end{bmatrix}, $$$$
u+v=\begin{bmatrix}
-4 \\
1\\
\end{bmatrix}, u-v=\begin{bmatrix}
2 \\
3\\
\end{bmatrix},
u-2v=\begin{bmatrix}
5 \\
4\\
\end{bmatrix}
$$
Graphing the vectors requires the first entry of the matrix to be taken as an x-coordinate and the second entry of the matrix to be taken as the y-coordinate, then graphing as an ordered pair (with an arrow).
