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: 30

Answer

Proof shown below

Work Step by Step

The $(i, j)$-entry in $(rA)B$ is $ra_{i1}b_{1j} + ... +ra_{in}b_{nj}$ The $(i, j)$-entry in $r(AB)$ is $r(a_{i1}b_{1j} + ... +a_{in}b_{nj})$ The $(i, j)$-entry in $A(rB)$ is $A(rb_{1j} + ... +rb_{nj})=(a_{i1}rb_{1j} + ... +a_{in}rb_{nj})$ Because the $(i, j)$-entries are all equal, the matrix products are also equal
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.