Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.4 - The Determinant of a Square Matrix - 10.4 Exercises - Page 744: 89

Answer

$e^{5x}$

Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{bmatrix}p & q \\r & s\end{bmatrix}$ After simplifying, the determinant of this matrix will be: $det =(e^{2x})(3e^{3x})-(2e^{2x})(e^{3x})$ or, $=3e^{5x}-2e^{5x}$ or, $=e^{5x}$
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