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: 25


a. No, 3 b. Yes, Infinite c. Yes, by the definition of linear combinations

Work Step by Step

a. There are only 3 vectors in the set $\{a_1,a_2,a_3\}$. Since $b$ is not one of these three vectors, it is not in the set. b. There are infinite vectors in the span of the three vectors due to their linear independence. Because all three vectors are linearly independent, the vectors span $\mathbf{R}^3$ and thus $b$ is in $W$. c. Yes, the third column is a linear combination of the three vectors with coefficients $0,0,1$, so it is in $W$.
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