Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises - Page 61: 4

Answer

Yes, the vectors are linearly independent.

Work Step by Step

According to the box on page 59, two vectors are linearly dependent if one is a constant multiple of the other. However, by multiplying the first vector by $2$, we can see that it is not a multiple of the second vector, since the first vector components are the same ($-2=-2$) but the second vector components are different ($8\neq-8$). Hence, the vectors cannot be linearly dependent: they must be linearly independent.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.