Answer
$-2e^{10t}$
Work Step by Step
We know that the determinant of a matrix \[
\left[\begin{array}{rr}
a & b \\
c &d \\
\end{array} \right]
\]
is $D=ad-bc$.
hence here $D=e^{6t}4e^{4t}-e^{4t}6e^{6t}=4e^{10t}-6e^{10t}=-2e^{10t}$
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 3 - Determinants - 3.1 The Definition of the Determinant - Problems - Page 207: 43
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