College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 8 - Section 8.4 - Matrix Algebra - 8.4 Assess Your Understanding - Page 598: 22

Answer

$\left[\begin{array}{ccc} {6}&{14}&{-14}\\ {2}&{27}&{-18}\\ {3}&{0}&{33}\end{array}\right]$

Work Step by Step

$CA=\left[\begin{array}{ccc} {1}&{14}&{-14}\\ {2}&{22}&{-18}\\ {3}&{0}&{28}\end{array}\right]\quad$(see sol. exercise 17) $5I_{3}=5\cdot\left[\begin{array}{lll} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{array}\right]=\left[\begin{array}{lll} 5 & 0 & 0\\ 0 & 5 & 0\\ 0 & 0 & 5 \end{array}\right]$ the sum is defined, as both are 3 by 3 matrices. $CA+5I_{3}=\left[\begin{array}{ccc} {1+5}&{14}&{-14}\\ {2}&{22+5}&{-18}\\ {3}&{0}&{28+5}\end{array}\right]=\left[\begin{array}{ccc} {6}&{14}&{-14}\\ {2}&{27}&{-18}\\ {3}&{0}&{33}\end{array}\right]$
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