Differential Equations and Linear Algebra (4th Edition)

by Goode, Stephen W.; Annin, Scott A.

Published by Pearson

ISBN 10: 0-32196-467-5

ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.6 Bases and Dimension - True-False Review - Page 308: e

Answer

False.

Work Step by Step

False, e.g. $S$ could contain $m$ parallel vectors, then it definitely doesn't span a vector space with dimension $n$.

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