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 - 2.7 Elementary Matrices and the LU Factorization - True-False Review - Page 186: c

Answer

False

Work Step by Step

Any invertible matrix is a product of elementary matrices. Conversely, since elementary matrices are invertible, a product of elementary matrices is a product of invertible matrices. Thus, the statement "A product of elementary matrices is an elementary matrix" is wrong since every invertible matrix can only be expressed as a product of elementary matrices.
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