Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.6 Exercises - Page 139: 13

Answer

$x=\left[\begin{array}{c}99576 \\ 97703 \\ 51231 \\ 131570 \\ 49488 \\ 329554 \\ 13835\end{array}\right]$

Work Step by Step

Find matrix $I-C$ : $I-C=\left[\begin{array}{ccccccc}0.8412 & -0.0064 & -0.0025 & -0.0304 & -0.0014 & -0.0083 & -0.1594 \\ -0.0057 & 0.7355 & -0.0436 & -0.0099 & -0.0083 & -0.0201 & -0.3413 \\ -0.0264 & -0.1506 & 0.6443 & -0.0139 & -0.0142 & -0.0070 & -0.0236 \\ -0.3299 & -0.0565 & -0.0495 & 0.6364 & -0.0204 & -0.0483 & -0.0649 \\ -0.0089 & -0.0081 & -0.0333 & -0.0295 & 0.6588 & -0.0237 & -0.0020 \\ -0.1190 & -0.0901 & -0.0996 & -0.1260 & -0.1722 & 0.7632 & -0.3369 \\ -0.0063 & -0.0126 & -0.0196 & -0.0098 & -0.0064 & -0.0132 & 0.9988\end{array}\right]$ We will put matrix $A=[I-C d]$ into matlab and row reduce it by using command rref $(A)$ Result is: \[ \begin{array}{llllllll} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 99576 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 97703 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 51231 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 131570 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 49488 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 329554 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 13835 \\ & & & 99576 & & \\ & & 97703 & & & \\ & & 51231 & & \\ \text { So, } x= & 131570 & & & \\ & & 49488 & & \\ & & & 329554 & & \\ & & & 13835 & & \end{array} \]
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