Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - Problems - Page 32: 8

Answer

$$w= 2v-u$$$$x=2v-2u$$ $$y=3.5v-2u$$ $$ z=4v-3u$$

Work Step by Step

Using the graph given in the textbook, follow the dotted grid lines to each point, w-z. For example, to get to point w, we could either go to the right two times (in the positive v direction) and down one time (in the negative u direction), or we could go down once (in the negative u direction) and then right two times (in the positive v direction). Either sequence yields that $$w=2v-u$$ Use this same strategy, following the grid lines, to find x-z: $$x=2v-2u$$ $$y=3.5v-2u$$ $$ z=4v-3u$$
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