Answer
False
Work Step by Step
According to Theorem 2.8.1, if the linear system $Ax = 0$ has a nontrivial solution,
then $A$ is not invertible. Hence, $A$ can't be expressed as a product of elementary matrices also.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 2 - Matrices and Systems of Linear Equations - 2.8 The Invertible Matrix Theorem I - True-False Review - Page 189: a
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