Answer
True
Work Step by Step
We have $X'=0\\
\rightarrow 2AX=0\\
\rightarrow AX=0$
The type of equilibrium point for the linear system $x′ = Ax$ is the same as the type of equilibrium point for the linear system $x′ = (2A)x$.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 9 - Systems of Differential Equations - 9.9 The Phase Plane for Linear Autonomous Systems - True-False Review - Page 653: e
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