Elementary Linear Algebra 7th Edition

Published by Cengage Learning
ISBN 10: 1-13311-087-8
ISBN 13: 978-1-13311-087-3

Chapter 2 - Matrices - 2.2 Properties of Matrix Operations - 2.2 Exercises - Page 61: 58

Answer

See proof below.

Work Step by Step

From the properties of matrices, we have that $(cd) A=(cd) [a_{ij}]$ , and c,d are real numbers Then, $(cd) A=(cd) [a_{ij}]= [(cd)a_{ij}] $ Since c,d and $a_{ij}$ are real numbers, then $(cd) A=(cd) [a_{ij}]= [(cd)a_{ij}]= [c(da_{ij}])=c[da_{ij}]=c(dA)$
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