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: 32


$S$ is a linearly dependent set of vectors.

Work Step by Step

Since one can have the combination $$(2,-1)=3(1,0)-(1,1)$$ then we get the non trivial combination $$(2,-1)-3(1,0)+(1,1)=(0,0).$$ Hence, $S$ is a linearly dependent set of vectors. Or, instead, since $R^2$ has dimension $2$ then the maximum number of linearly independent vectors is $2$ but $S$ has $3$ vectors then it must be linearly dependent.
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