3.9. Is the reduced echelon form of a matrix unique? Justify your conclusion.Namely, suppose that by performing some row operations (not necessarily fol-lowing any algorithm) we end up with a reduced echelon matrix. Do we alwaysend up with the same matrix, or can we get different ones? Note that we are onlyallowed to perform row operations, the "column operations"' are forbidden.

The row reduced echelon form of a matrix is unique .

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Is the reduced echelon form of a matrix unique? Justify your conclusion.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 3CEXP

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3.9. Is the reduced echelon form of a matrix unique? Justify your conclusion.
Namely, suppose that by performing some row operations (not necessarily fol-
lowing any algorithm) we end up with a reduced echelon matrix. Do we always
end up with the same matrix, or can we get different ones? Note that we are only
allowed to perform row operations, the "column operations"' are forbidden.

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