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: 28

Answer

The pivot columns must be the columns of the coefficient matrix.

Work Step by Step

If the pivot columns are the columns of the coefficient matrix, then the last column (on the right) of the augmented matrix is not a pivot column, which means the system is consistent. Also, if the pivot columns are the columns of the coefficient matrix, then all the columns of the coefficient matrix are pivot columns. From the previous problem, we know that for a consistent system, if all the columns of the coefficient matrix are pivot columns, then the system has a unique solution.
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