Consider the First-Order Homogeneous System of Linear Differential Equations
$\left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \\ \cos (6 t) & \sin (6 t)\end{array}\right\}$

Multiple Choice

Consider the first-order homogeneous system of linear differential equations
= x
Which of these is a fundamental set of solutions for this system?

A) $\left\{\begin{array}{ll}-\sin (6 t) & \cos (6 t) \\ \cos (6 t) & \sin (6 t) \end{array}\right\}$
B) $\left\{\begin{array}{ll}\sin (6 t) & -\cos (6 t) \\ \cos (6 t) & \sin (6 t) \end{array}\right\}$
C) $\left\{\begin{array}{ll}\sin (36 t) & -\cos (36 t) \\ \cos (36 t) & \sin (36 t) \end{array}\right\}$
D) $\left\{\begin{array}{ll}e^{6 t} & -e^{-6 t} \\ e^{6 t} & e^{-6 t}\end{array}\right\}$
E) $\left\{\begin{array}{ll}e^{6 t} & e^{-6 t} \\ -e^{6 t}, & e^{-6 t}\end{array}\right\}$