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 - 1.1 Exercises: 31


Add $-4$ times row (1) to row (3) to transform the first matrix into the second matrix. To reverse this operation, add $+4$ of row (1) to row (3) in the second matrix to get back the original matrix.

Work Step by Step

Recall from the bottom of page 6 and the top of page 7 that all elementary row operations are reversible. Moreover, there are only three such operations: (1) swapping two rows, (2) multiplying a row by a nonzero constant, and (3) adding a constant multiple of one row to another row.
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