Linear Algebra and Its Applications (5th Edition)

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

Chapter 2 - Matrix Algebra - 2.8 Exercises - Page 154: 32

Answer

See solution

Work Step by Step

Because Nul R is not the zero subspace, Rx=0 has nontrivial solutions. This means R does not have a pivot in every row or every column. Because R doesn't have a pivot in every column, Col R does not span $R^6$ and its basis has fewer than 6 vectors.
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