Consider the First-Order Homogeneous System of Linear Differential Equations
$\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)$

Multiple Choice

Consider the first-order homogeneous system of linear differential equations

Select the vectors from this list that, together, constitute a fundamental set of solutions for this system.

A) $\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)$
B) $\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$
C) $\left[\begin{array}{l}-\cos (6 t) \\ \sin (6 t) \\ \cos (6 t) \end{array}\right)$
D) $\left(\begin{array}{l}\cos (6 t) \\ \sin (6 t) \\ -\cos (6 t) \end{array}\right)$
E) $\left(\begin{array}{l}\sin (6 t) \\ \cos (6 t) \\ -\cos (6 t) \end{array}\right)$
F) $\left(\begin{array}{l}\sin (6 t) \\ \cos (6 t) \\ -\sin (6 t) \end{array}\right)$
G) $\left[\begin{array}{l}-\sin (6 t) \\ \cos (6 t) \\ \sin (6 t) \end{array}\right)$