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 - Page 23: 31


Yes, such a system can be consistent. For example: $$ \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 2 \\ \end{bmatrix} $$

Work Step by Step

As long as the excess rows are linear combinations of the non-excess rows, the system is consistent. In the example above, the third equation provides no information that is not contained in the first two, but it does not contradict them either. Thus, the matrix is both overdetermined and consistent.
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