For which of the following systems is the origin a degenerate node?
A) $ \mathbf{x}^{\prime}=\left(\begin{array}{ll}2022 & 5 \ 0 & -7\end{array}\right) \mathbf{x} $
B) $ x^{\prime}=\left(\begin{array}{ll}-2022 & 20 \ 0 & -5\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}5 & -4 \ 4 & 0\end{array}\right) \mathbf{x} $
E) $ \mathbf{x}^{\prime}=\left(\begin{array}{cc}0 & 4 \ -1 & 0\end{array}\right) \mathbf{x} $

Question

Quizplus · Accepted Answer

The origin is a degenerate node when both eigenvalues are equal. In this case, the eigenvalues are both 2022, so the origin is a degenerate node.

For Which of the Following Systems Is the Origin a Degenerate