Question

\[x'\left(\begin{matrix}3&-2\\4&-1\end{matrix}\right)x\]

Answer 1

now your just making stuff up ....

Answer 2

I got \(\lambda = 1\pm 2i\) that leads to solution
\[x_1= C_1e^t cos 2t- C_2 e^t sin 2t\\x_2= C_1e^t sin 2t+C_2e^t cos 2t\]
so, the combination should be \[x(t) = C_1 e^t \left(\begin{matrix}cos 2t\\sin2t\end{matrix}\right)\] + something else
but the solution from book is not that

Answer 3

they said
x(t) = \[C_1 e^t \left(\begin{matrix}cos 2t\\cos 2t+sin2t\end{matrix}\right)+C_2 e^{2t}\left(\begin{matrix}sin2t\\-cos2t+sin2t\end{matrix}\right)\]

Answer 4

why? @oldrin.bataku

Answer 5

another question, we have formula to get the answer, why do we have break it down to real and imaginary solution, then combine them again ?? why do we have to find eigenvectors and proceed the loonnnng stuff to get that answer?

Answer 6

Ok, let it aside, teach me how to find eigenvalue of this