Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 4 - Vector Spaces - 4.5 Basis and Dimension - 4.5 Exercises - Page 188: 72


(a) True. (b) False.

Work Step by Step

(a) True. This by Theorem 4.10. (b) False. This is not true. For example, $W=\{(1,1,1), (2,2,2)\}$ is a subset of $R^3$ which is is a vector space of dimension $3$, however, $W$ is a linearly dependent set of vectors.
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