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 - Review Exercises - Page 221: 1


(a) \begin{align*} (0,2,5). \end{align*} (b) \begin{align*} (2,0,4). \end{align*} (c) \begin{align*} (-2,2,14). \end{align*} (d) \begin{align*} (-5,6,5). \end{align*}

Work Step by Step

Consider the vectors ${u}=(-1,2,3), \quad {v}=(1,0,2)$ (a) \begin{align*} u+v &=(-1,2,3)+(1,0,2)\\ &=(0,2,5). \end{align*} (b) \begin{align*} v &=2(1,0,2)\\ &=(2,0,4). \end{align*} (c) \begin{align*} u-v &=(-1,2,3)-(1,0,2)\\ &=(-2,2,14). \end{align*} (d) \begin{align*} 3u-2v &=3(-1,2,3)-2(1,0,2)\\ &=(-3,6,9)-(2,0,4)\\ &=(-5,6,5). \end{align*}
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