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The general solution of the system:

$$X'=\left(\begin{array}{cc} 5 & -1 \\\ 0 & 3\end{array}\right)X$$

...is given by:

A

$X=c_{1}\left(\begin{array}{c}1 \\\ 0 \end{array}\right)e^{3t}+c_{2}\left(\begin{array}{c}1 \\\ 2 \end{array}\right)e^{5t}$

B

$X=c_{1}\left(\begin{array}{c}1 \\\ 0 \end{array}\right)e^{3t}+c_{2}\left(\begin{array}{c}1 \\\ -2 \end{array}\right)e^{5t}$

C

$X=c_{1}\left(\begin{array}{c}1 \\\ 2 \end{array}\right)e^{3t}+c_{2}\left(\begin{array}{c}1 \\\ 0 \end{array}\right)e^{5t}$

D

$X=c_{1}\left(\begin{array}{c}1 \\\ 2 \end{array}\right)e^{-3t}+c_{2}\left(\begin{array}{c}1 \\\ 0 \end{array}\right)e^{-5t}$

E

None of the above

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