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 - 4.4 Spanning Sets and Linear Independence - 4.4 Exercises - Page 178: 34

Answer

$S$ is linearly independent.

Work Step by Step

Assume the combination $$a(6,2,1)+b(-1,3,2)=(0,0,0).$$ We have the system \begin{align*} 6a-b&=0\\ 2a+3b&=0\\ a+2b&=0. \end{align*} The above system has a unique solution, that is, $$a=0, \quad b=0.$$ Consequently, $S$ is linearly independent.
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