Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.1 Exercises - Page 103: 22

Answer

The columns of AB are linearly dependent.

Work Step by Step

Assume the columns of B are linearly dependent. Then there exists a nonzero vector x such that Bx=0. A*Bx=A*0 A*Bx=0 (AB)x=0 Since x is nonzero. the columns of AB are linearly dependent.
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