Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 0-32198-238-X
ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.3 Exercises: 24


a. True b. True c. False d. True e. True

Work Step by Step

a. True, this is the definition of a vector b. True, by the algebraic properties of vectors: $(u-v)+v = (u + (-v)) + v = u + (-v + v) =u$ c. False, the zero vector is always in the span of a set of vectors. d. True, the line through $u$ and the origin, is the vectors formed by a linear combination of $u$ and $v$ where the coefficient on $u$ is any real number and the coefficient on $v$ is $0$. e. True, this follows from the definition of span
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