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 743: 83



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, this matrix yields: $4=(x)(x+1) - (2)(-1) $ or, $x^2+x-2=0$ or, $(x^2+x+\dfrac{1}{4})-2=0+\dfrac{1}{4}$ or, $(x+\dfrac{1}{4})^2=\dfrac{9}{4} \implies x=-\dfrac{1}{2} \pm \sqrt{\dfrac{9}{4}}$ So, $x=1,-2$
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