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 - 5.3 Orthonormal Bases: Gram-Schmidt Process - 5.3 Exercises - Page 257: 11


(a) the set is orthogonal. (b) the set is not orthonormal. (c) the set is not a basis for $R^3$.

Work Step by Step

Let $u=(2,5,-3)$ and $v=(4,2,6)$, then we have (a) since $u\cdot v=8+10-18=-0$, then the set is orthogonal. (b) since $\|u\|=4+25+9=38\neq 1$, then the set it is not orthonormal. (c) sine $R^3$ has dimension $3$ and the set has two vectors, then it is not a basis for $R^3$.
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