Linear Algebra and Its Applications (5th Edition)

by Lay, David C.; Lay, Steven R.; McDonald, Judi J.

Published by Pearson

ISBN 10: 032198238X

ISBN 13: 978-0-32198-238-4

Chapter 1 - Linear Equations in Linear Algebra - 1.4 Exercises - Page 42: 35

Answer

The equation Ax = 5z is consistent because 5y is a solution of Ax = 5z.

Work Step by Step

Suppose that y and z satisfy Ay = z. Then 5z = 5Ay. By Theorem 5(b), 5Ay = A(5y). So 5z = A(5y), which shows that 5y is a solution of Ax = 5z. Thus, the equation Ax = 5z is consistent.

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