Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 5 - Inner Product Spaces - Review Exercises - Page 284: 34


$$\operatorname{proj}_{{v}} {u} =(0,5).$$

Work Step by Step

Let $u=(2,5)$, $v=(0,5)$, $\langle{u}, {v}\rangle=u\cdot v$. Then, we have $$\langle{u}, {v}\rangle=25, \quad \langle{v}, {v}\rangle=25.$$ Now, the orthogonal projection of $u$ onto $v$ is given by $$\operatorname{proj}_{{v}} {u} =\frac{\langle{u}, {v}\rangle}{\langle{v}, {v}\rangle} {v}=\frac{25}{25}(0,5)=(0,5).$$
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.