Answer
$\begin{bmatrix}
5
\\
4
\\
2
\end{bmatrix}$
Work Step by Step
The additive inverse of $G=
\begin{bmatrix}
-2
\\0
\\5\end{bmatrix}
$ is
\begin{align*}
&
-1\begin{bmatrix}
-2
\\0
\\5
\end{bmatrix}
\\\\&=
\begin{bmatrix}
-1(-2)
\\
-1(0)
\\
-1(5)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
2
\\
0
\\
-5
\end{bmatrix}
.\end{align*}
With $E=
\begin{bmatrix}
3
\\
4
\\
7
\end{bmatrix}
,$ by adding the corresponding elements, the sum of $E$ and the inverse of $G$ is
\begin{align*}
&\begin{bmatrix}
3
\\
4
\\
7
\end{bmatrix}
+
\begin{bmatrix}
2
\\
0
\\
-5
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3+2
\\
4+0
\\
7+(-5)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
5
\\
4
\\
2
\end{bmatrix}
.\end{align*}
