Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.2 Exercises: 29

Answer

There must exist free variables.

Work Step by Step

If there are fewer equations than unknowns, then that means that the number of rows of the augmented matrix is less than the number of columns minus one. Thus, there must be at least one column without a pivot entry. This means that there is a free variable, and given that the system is consistent, this means that there are an infinite number of solutions.
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