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 - 4.1 Vectors in Rn - 4.1 Exercises - Page 153: 28

Answer

(a) $u$ is a scalar multiple of $z$. (b) $v$ is a scalar multiple of $z$.

Work Step by Step

(a) since $u=\left(2,4,9\right)=12 \left(\frac{1}{2},-\frac{2}{3},\frac{3}{4}\right)$, then $u$ is a scalar multiple of $z$. (b) since $v=\left(-1,\frac{4}{3},-\frac{3}{2}\right)=-2 \left(\frac{1}{2},-\frac{2}{3},\frac{3}{4}\right)$, then $v$ is a scalar multiple of $z$.
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