Answer
See proof below.
Work Step by Step
From the properties of matrices and that $c$ , $d$ are real values, we get:
$(c+d)A=(c+d)[a_{ij}]=[(c+d)a_{ij}]=[c* a_{ij}+d* a_{ij}]=[c* a_{ij}]+[d* a_{ij}]=c*[a_{ij}]+d*[a_{ij}]=cA+dA$
Elementary Linear Algebra 7th Edition
by Larson, Ron
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: 60
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