Answer
True
Work Step by Step
From the Theorem 9.8.2 we have:
$\frac{d}{dt}(e^{At})=\frac{d}{dt}(1+At+\frac{(At)^2}{2!}+....)=Ae^{At}$
The derivative of the matrix exponential function $e^{At}$ with respect to the variable $t$ is $Ae^{At}$$
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 - 9.8 Matrix Exponential Function and Systems of Differential Equations - True-False Review - Page 642: a
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