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: 46

Answer

$-5$

Work Step by Step

The determinant of a $2 \times 2$ matrix can be computed by using the formula $det =ps-qr$ where $det =\begin{vmatrix}p & q \\r & s\end{vmatrix}$ So, $\begin{vmatrix} 1& 0 &0 \\-4 & -1 & 0 \\ 5 &1 & 5\end{vmatrix}=1 \begin{vmatrix} -1 & 0 \\1 & 5\end{vmatrix}$ or, $=1[(-1)(5)-0]$ or, $=-5$
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