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 712: 100b


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. When given the following conditions, the matrix will be: $\begin{bmatrix} 1 & n \\ 0 & 1 \\ \end{bmatrix}$ where $n \ne 0$ The above matrix satisfies rules 1 - 3 but not rule 4, so the matrix is in row-echelon form.
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