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 - Review Exercises - Page 284: 7


(a) $\| u \| = \sqrt{7}$ (b) $\| v \| =\sqrt{7}$ (c) $\langle u, v \rangle = 6$ (d) $d(u,v) =\sqrt{2}.$

Work Step by Step

Let $u=(0,1,-1,1,2), \quad v=(0,1,-2,1,1)$, then we have (a) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2+u_3^2+u_4^2+u_5^2}=\sqrt{7}$ (b) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2+v_4^2+v_5^2}=\sqrt{7}$ (c) $\langle u, v \rangle =u_1v_1+u_2v_2+u_3v_3+u_4v_4+u_5v_5= 6$ (d) $d(u,v)=\| u-v \|=\| (0,0,1,0,1) \|=\sqrt{2}.$
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