Complex Eigenvalues of system of DE

[member 731016]

Homework Statement

Please see below.

Relevant Equations

Please see below

For this problem,

Can someone please explain to me how they got from the orange step to the yellow step?

I am confused how the two expressions are equivalent.

Thanks!

 

[Orodruin]

Just perform the multiplications and collect real and imaginary terms in their own matrices.

 

[renormalize]

I am confused how the two expressions are equivalent.

The yellow expression contains a sign error; the second term should be:$$
i\left(\begin{array}{c}
-e^{-2t}\sin3t\\
+e^{-2t}\cos3t
\end{array}\right)
$$

 

[member 731016]

Thank you for your replies @Orodruin and @renormalize ! Yeah that was part of my confusion is that there is a typo

It makes sense now that I know it is a typo!

Thanks!