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: 90



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: $det =(e^{-x})((1-x)e^{-x})+(e^{-x})x(e^{-x})$ or, $=e^{-2x}-xe^{-2x}+xe^{-2x}$ or, $=e^{-2x}$
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