Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.1 Exercises - Page 11: 33

Answer

$4T_{1}-T_{2}-T_{4}=30$ $-T_{1}+4T_{2}-T_{3}=60$ $-T_{2}+4T_{3}-T_{4}=70$ $-T_{1}-T_{3}+4T_{4}=40$

Work Step by Step

We omit degree symbols for convenience. Since each node's temperature is the average of the temperatures at the four surrounding nodes, we simplify the following four equations to get the system above: $T_{1}=\frac{10+20+T_{2}+T_{4}}{4}$ $T_{2}=\frac{T_{1}+20+40+T_{3}}{4}$ $T_{3}=\frac{T_{4}+T_{2}+40+30}{4}$ $T_{4}=\frac{10+T_{1}+T_{3}+30}{4}$
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