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: 7

Answer

$$a= u-2v$$$$b=2u-2v$$ $$c=2u-3.5v$$ $$ d=3u-4v$$

Work Step by Step

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