Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 2 - Matrices and Systems of Linear Equations - 2.4 Row-Echelon Matrices and Elementary Row Operations - Problems - Page 155: 5



Work Step by Step

A matrix is a row-echelon matrix if: 1. If there are any rows consisting only of zeros, they are all together at the bottom of the matrix. 2. The first nonzero element in any nonzero row is a $1$. 3. The leading $1$ of any row below the first row is to the right of the leading $1$ of the row above it. A matrix is a reduced row-echelon matrix if it is a row-echelon matrix and any column that contains a leading $1$ has zeros everywhere else. Hence here we can see it is in row-echelon form but the first row has other non-zero elements apart from its leading $1$ thus it is not in reduced row-echelon form.
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