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: 23


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

Work Step by Step

a. False, row and column vectors are distinct and typically represent different things. b. False, the two vectors are linearly independent, so they do not lie on the same line. c. True, a linear combination may be a multiple of $v_1$ added to $0$ times $v_2$. d. True, this follows from the equivalence of vector equations and augmented matrices. The two are merely different representations of the same system. e. False, the span can sometimes be a line or a point. In addition, in higher dimensional space, it can be other spaces of higher dimensionality than a plane.
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