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: 2

Answer

(a) \begin{align*} (-1,3,2). \end{align*} (b) \begin{align*} (0,2,2). \end{align*} (c) \begin{align*} (-1,1,0). \end{align*} (d) \begin{align*} (-3,4,1). \end{align*}

Work Step by Step

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