Complex Eigenvalues of system of DE

  • #1
member 731016
Homework Statement
Please see below.
Relevant Equations
Please see below
For this problem,
1715292619315.png

1715292474940.png

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!
 

Attachments

  • 1715292574625.png
    1715292574625.png
    17.4 KB · Views: 6
Physics news on Phys.org
  • #2
Just perform the multiplications and collect real and imaginary terms in their own matrices.
 
  • Like
  • Love
Likes member 731016 and FactChecker
  • #3
ChiralSuperfields said:
I am confused how the two expressions are equivalent.
The yellow expression contains a sign error; the second term should be:$$
i\left(\begin{array}{c}
-e^{-2t}\sin3t\\
+e^{-2t}\cos3t
\end{array}\right)
$$
 
  • Love
Likes member 731016
  • #4
Thank you for your replies @Orodruin and @renormalize ! Yeah that was part of my confusion is that there is a typo
1715294433735.png

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

Thanks!
 

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
402
  • Calculus and Beyond Homework Help
Replies
4
Views
457
  • Calculus and Beyond Homework Help
Replies
5
Views
496
  • Calculus and Beyond Homework Help
Replies
6
Views
420
  • Calculus and Beyond Homework Help
Replies
7
Views
990
  • Calculus and Beyond Homework Help
Replies
27
Views
532
  • Calculus and Beyond Homework Help
Replies
2
Views
662
  • Calculus and Beyond Homework Help
Replies
2
Views
390
  • Calculus and Beyond Homework Help
Replies
2
Views
282
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
Back
Top