Answer
See solution
Work Step by Step
u, v, and w are vectors and c is a scalar.
Theorem 1. b.
$(u+v)\cdot w=(u+v)^Tw=(u^T+v^T)w=u^Tw+v^Tw=u\cdot w+v\cdot w$
Theorem 1. c.
$(cu)\cdot v=(cu)^Tv=c(u^T)v=c(u\cdot v)=c(u^T)v=(u^T)(cv)=u\cdot(cv)$
Linear Algebra and Its Applications (5th Edition)
by Lay, David C.; Lay, Steven R.; McDonald, Judi J.
Published by
Pearson
ISBN 10:
032198238X
ISBN 13:
978-0-32198-238-4
Chapter 6 - Orthogonality and Least Squares - 6.1 Exercises - Page 339: 21
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