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 187: 37


$S$ is not a basis for $R^3$.

Work Step by Step

The set $S=\{(0,3,-2),(4,0,3),(-8,15,-16)\}$ is not a basis for $R^3$ because $S$ is not linearly independent. For example, one can see that $$(-8,15,-16)=5(0,3,-2)-2(4,0,3).$$ Which means that $S$ is linearly dependent set of vectors.
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