Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.8 Applications of Vector Spaces - 4.8 Exercises - Page 219: 21

Answer

$$W=2 \mathrm{e}^{x} \mathrm{e}^{2 x}.$$

Work Step by Step

The Wronskian of \left\{1, e^{x}, e^{2 x}\right\} is given by $$W=\left|\begin{array}{ccc}1 &\mathrm{e}^{x} &\mathrm{e}^{2 x}\\ 0& \mathrm{e}^{x} &2\mathrm{e}^{2 x}\\ 0& \mathrm{e}^{x} &4 \mathrm{e}^{2 x}\end{array}\right|=2 \mathrm{e}^{x} \mathrm{e}^{2 x}.$$
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