Linear Algebra and Its Applications (5th Edition)

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

Chapter 6 - Orthogonality and Least Squares - 6.1 Exercises - Page 338: 9

Answer

$\vec{u}=\begin{bmatrix} -3/5\\ 4/5 \end{bmatrix}$

Work Step by Step

$\vec{v}=\begin{bmatrix} -30\\ 40 \end{bmatrix}$ $||\vec{v}||=\sqrt{\vec{v}\cdot\vec{v}}=\sqrt{(-30)^2+40^2}=50$ $\vec{u}=\frac{\vec{v}}{||\vec{v}||}=\begin{bmatrix} -3/5\\ 4/5 \end{bmatrix}$
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