Differential Equations and Linear Algebra (4th Edition)

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



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 $D=e^{6t}4e^{4t}-e^{4t}6e^{6t}=4e^{10t}-6e^{10t}=-2e^{10t}$
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