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: 21

Answer

$\left[\begin{array}{ll} 25 & -9\\ 4 & 20 \end{array}\right]$

Work Step by Step

We found $AC$ is problem 15: $ AC =\begin{bmatrix} 28 & -9\\ 4 & 23 \end{bmatrix}$ Next, calculate $3$ times the identity matrix: $3I=3 \begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}=\begin{bmatrix} 3 & 0\\ 0 & 3 \end{bmatrix}$ Now, find the difference: $AC-3I=\begin{bmatrix} 28 & -9\\ 4 & 23 \end{bmatrix} \begin{bmatrix} 3 & 0\\ 0 & 3 \end{bmatrix} \\=\left[\begin{array}{ll} 28-3 & -9-0\\ 4-0 & 23-3 \end{array}\right] \\=\left[\begin{array}{ll} 25 & -9\\ 4 & 20 \end{array}\right]$
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