Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.4 Matrix Algebra - 10.4 Assess Your Understanding - Page 777: 26

Answer

$\begin{bmatrix} {-22}&{29}&{8}&{-1}\\ {-10}&{17}&{6}&{-1}\end{bmatrix}$

Work Step by Step

Since $A$ is a $2 \times 2 $ matrix and $B$ is a $2 \times 4$ matrix, the product $AB$ is defined as a $2 \times 4$ matrix. $AB=\begin{bmatrix} (4)(-6)+(1)(2) & (4)(6)+(1)(5) & (4)(1)+(1)(4) & (4)(0)+(1)(-1)\\ (2)(-6)+(1)(2) & (2)(6)+(1)(5) & (2)(1)+(1)(4) & (2)(0)+(1)(-1) \end{bmatrix}\\=\begin{bmatrix} -24+2 & 24+5 & 4+4 & 0+(-1)\\ -12+2 & 12+5 & 2+4 & 0+(-1) \end{bmatrix} \\=\begin{bmatrix} {-22}&{29}&{8}&{-1}\\ {-10}&{17}&{6}&{-1}\end{bmatrix}$
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