For which of the following systems is every solution periodic?
A) $ \mathbf{x}^{\prime}=\left(\begin{array}{ll}2022 & -25 \ 0 & -4\end{array}\right) \mathbf{x} $
B) $ x^{\prime}=\left(\begin{array}{ll}-2022 & -60 \ 0 & -4\end{array}\right) x $
C) $ \mathbf{x}^{\prime}=\left(\begin{array}{ll}2022 & 0 \ 0 & 2022\end{array}\right) \mathbf{x} $
D) $ x^{\prime}=\left(\begin{array}{ll}4 & -3 \ 3 & 0\end{array}\right) x $
E) $ \mathbf{x}^{\prime}=\left(\begin{array}{cc}0 & 1 \ -3 & 0\end{array}\right) \mathbf{x} $

Question

Quizplus · Accepted Answer

The system in choice E has purely imaginary eigenvalues, which implies that every solution is periodic.

For Which of the Following Systems Is Every Solution Periodic x′=(2022−250−4)x \mathbf{x}^{\prime}=\left(\begin{array}{ll}2022 & -25 \\ 0 & -4\end{array}\right) \mathbf{x} x′=(20220​−25−4​)x

For Which of the Following Systems Is Every Solution Periodic $\mathbf{x}^{\prime}=\left(\begin{array}{ll}2022 & -25 \\ 0 & -4\end{array}\right) \mathbf{x}$