Consider the First-Order Homogeneous System of Linear Differential Equations
$\lambda=3, \xi=\left(\begin{array}{c}0 \\ -1\end{array}\right)$

Consider the first-order homogeneous system of linear differential equations

Select all of the correct eigenvalue-eigenvector pairs from the following choices.

A) $\lambda=3, \xi=\left(\begin{array}{c}0 \\ -1\end{array}\right)$
B) $\lambda=-3, \xi=\left(\begin{array}{l}0 \\ 1\end{array}\right)$
C) $\lambda=8, \xi=\left(\begin{array}{l}10 \\ 5\end{array}\right)$
D) $\lambda=8, \xi=\left(\begin{array}{l}10 \\ -5\end{array}\right)$
E) $\lambda=-3, \xi=\left(\begin{array}{l}1 \\ 0\end{array}\right)$
F) $\lambda=8, \xi=\left(\begin{array}{c}-5 \\ 10\end{array}\right)$