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: 30

Answer

$\begin{bmatrix} {6}&{32}\\ {1}&{3}\\ {-2}&{-4}\end{bmatrix}$

Work Step by Step

Since $A$ is a $3 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, the product $AB$ is defined as a $3 \times 2$ matrix. $$AB=\begin{bmatrix} {(4)(2)+(-2)(1)+3(0)}&{4(6)+(-2)(-1)+3(2)}\\ {0(2)+(1)(1)+(2)(0)}&{0(6)+(1)(-1)+(2)(2)}\\ {(-1)(2)+0(1)+1(0)}&{(-1)(6)+0(-1)+1(2)}\end{bmatrix} \\=\begin{bmatrix} {8-2+0}&{24+2+6}\\ {0+1+0}&{0-1+4}\\ {-2+0+0}&{-6+0+2}\end{bmatrix} \\=\begin{bmatrix} {6}&{32}\\ {1}&{3}\\ {-2}&{-4}\end{bmatrix}$$
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