Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 10 - 10.1 - Matrices and Systems of Equations - 10.1 Exercises - Page 710: 42


The matrix is not in Row-Echelon Form.

Work Step by Step

There are 3 main rules for a matrix to be in row echelon form: 1. A row of all 0s must be at the bottom. 2. The first non-zero entry in a row must be a 1. This is called the leading 1. 3. The leading 1 in a higher row must be in a column further to the left than a lower leading 1. For a matrix to be in reduced row echelon form, the rules for row echelon form must be met with the addition of this rule: 4. Every column with a leading 1 must have all 0s above the leading 1. Rule 3 is not followed because in row 3, the leading one is in the same column as the leading 1 above it. To follow the rule, the leading 1 in row 3 must be to the right of the leading one in row 2. The matrix is not in Row-Echelon Form.
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