?

Differential Equations

Free Version

Upgrade subject to access all content

Easy

Linear System with Complex Eigenvalues: Wronskian at $t=1$

DIFFEQ-WHRJOO

Consider the the linear system about $x=x(t)$: $x'=Ax$ where
$A=\left(\begin{array}{cc}1&2\\\ -3&2\end{array}\right)$. Suppose $\Phi$ is a fundamental matrix such that the Wronskian at $t=0$ is $det(\Phi(0))=2$.

Then, what is the value of $det(\Phi(1))$, the Wronskian at $t=1$?

A

$2$

B

$2e^{-3}$

C

$2e^{3}$

D

$1$