Find the complex conjugate eigenvalues and the corresponding eigenvectors of the matrix.
$$
\begin{bmatrix}
0 & -13 \\
13 & 0
\end{bmatrix}
$$
The eigenvalue(s) is/are.
(Type an exact answer, using radicals and ias needed. Use a comma to separate answers as needed.)
Find an eigenvector corresponding to the eigenvalue a + bi, where b>0. Choose the correct answer below.
A.
$$
\begin{bmatrix}
1-i \\
1
\end{bmatrix}
$$
B.
$$
\begin{bmatrix}
-i \\
1
\end{bmatrix}
$$
C.
$$
\begin{bmatrix}
i \\
1
\end{bmatrix}
$$
D.
$$
\begin{bmatrix}
1 \\
1
\end{bmatrix}
$$
E.
$$
\begin{bmatrix}
-1 \\
1
\end{bmatrix}
$$
F.
$$
\begin{bmatrix}
1+i \\
1
\end{bmatrix}
$$
Find an eigenvector corresponding to the eigenvalue a + bi, where b <0. Choose the correct answer below.
A.
$$
\begin{bmatrix}
i \\
1
\end{bmatrix}
$$
B.
$$
\begin{bmatrix}
-i \\
1
\end{bmatrix}
$$
