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 - 5.1 Length and Dot Product in Rn - 5.1 Exercises - Page 235: 23


(a) $-6.$ (b) $13.$ (c) $25.$ (d) $(-12,18).$ (e) $-30.$

Work Step by Step

Since $\mathbf{u}=(3,4), \quad \mathbf{v}=(2,-3)$, then we have (a) $\mathbf{u} \cdot \mathbf{v}=6-12=-6.$ (b) $\mathbf{v} \cdot \mathbf{v}=4+9=13.$ (c) $\|u\|^2=\mathbf{u} \cdot \mathbf{u}=9+16=25.$ (d) $(\mathbf{u} \cdot \mathbf{v})v=-6(2,-3)=(-12,18).$ (e) $\mathbf{u} \cdot \mathbf{(5v)}=(3,4)\cdot (10,-15) =30-60=-30.$
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