Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.5 - Determinants and Cramer's Rule - Concept and Vocabulary Check - Page 945: 1

Answer

$\left| \begin{matrix} 5 & 4 \\ 2 & 3 \\ \end{matrix} \right|=\underset{\scriptscriptstyle-}{5}\cdot \underset{\scriptscriptstyle-}{3}-\underset{\scriptscriptstyle-}{4}\cdot \underset{\scriptscriptstyle-}{2}=\underline{15}-\underset{\scriptscriptstyle-}{8}=\underset{\scriptscriptstyle-}{7}$ The value of this second-order determinant is 7.

Work Step by Step

$\text{For any determinant,}$ $\left| \begin{matrix} a & b \\ c & d \\ \end{matrix} \right|=ad-bc$ $\text{then for the given determinant}$ $\begin{align} & \left| \begin{matrix} 5 & 4 \\ 2 & 3 \\ \end{matrix} \right|=5\cdot 3-4\cdot 2 \\ & =15-8 \\ & =7 \end{align}$
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