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 - Page 33: 26


a. Yes b. the third column of A is a linear combination of the columns of A

Work Step by Step

a. Yes, because the columns of $A$ are linearly independent. b. All linear combinations of A's columns can be represented as $x_1a_1 + x_2a_2 + x_3a_3$. $a_3 = 0a_1 + 0a_2 + 1a_3$, thus it is a linear combination of the columns of A, and thus it is in $W$.
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