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: 35

Answer

S is not linearly independent.

Work Step by Step

Since $(3,3,3)=(1,1,1)+(2,2,2)$, then we have the non trivial combination $$(3,3,3)-(1,1,1)-(2,2,2)=(0,0,0).$$ Which means that the vectors are linearly dependent and hence $S$ is not linearly independent.
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