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: 80



Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{vmatrix}p & q \\r & s\end{vmatrix}$ $det=(a+b)\begin{vmatrix}a+b &a \\a & a+b\end{vmatrix}-a \begin{vmatrix}a & a \\a & a+b\end{vmatrix}+a \begin{vmatrix}a & a \\a+b & a\end{vmatrix}$ or, $=(a+b) [a^2+2ab+b^2-a^2]-a[a^2+ab-a^2] +a [a^2-a^2-ab]$ or, $=2a^2b+ab^2+2ab^2+b^3-2a^2b$ or, $=b^2(3a+b)$
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