Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.5 Exercises - Page 49: 39

Answer

Note that we can factor scalars out of equations; thus, $A(cu) = c(Au)$ We are given that $Au = 0$; thus, $A(cu) = c(Au) = c * 0 = 0$. Thus, we have shown $A(cu) = 0$ and that $cu$ also satisfied the equation $Ax = 0$.

Work Step by Step

Answer contains full explanation; see answer above.
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