Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises: 7

Answer

No, the columns of this matrix do not form a linearly independent set.

Work Step by Step

Theorem 8 states that if a set contains more vectors than entries in each vector, then the set is not linearly independent. In this case, there are 4 column vectors, but each vector contains only 3 entries. Equivalently, we can observe that not every column can be a pivot column, since a matrix cannot contain more pivots than rows.
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