Consider the First-Order Homogeneous System of Linear Differential Equations
$\mathbf{x}(t)=C_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{-7 t}+C_{2}\left(\begin{array}{c}-7 \\ 9\end{array}\right) e^{9 t}$

Multiple Choice

Consider the first-order homogeneous system of linear differential equations

Which of these is the general solution of the system? Here, C₁ and C₂ are arbitrary real constants.

A) $\mathbf{x}(t) =C_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{-7 t}+C_{2}\left(\begin{array}{c}-7 \\ 9\end{array}\right) e^{9 t}$
B) $x(t) =C_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{7 t}+C_{2}\left(\begin{array}{c}7 \\ -9\end{array}\right) e^{-9 t}$
C) $\mathbf{x}(t) =C_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{7 t}+C_{2}\left(\begin{array}{c}-7 \\ 9\end{array}\right) e^{9 t}$
D) $\mathbf{x}(t) =C_{1}\left(\begin{array}{l}1 \\ 1\end{array}\right) e^{-7 t}+C_{2}\left(\begin{array}{c}7 \\ -9\end{array}\right) e^{-9 t}$
E) $\mathbf{x}(t) =C_{1}\left(\begin{array}{l}1 \\ 0\end{array}\right) +C_{2}\left(\begin{array}{c}7 \\ -9\end{array}\right) e^{-9 t}$