Answer
$S$ is not a subspace.
Work Step by Step
If $x=y=z=0$, then $x-y+z\neq 1$ and hence $S$ does not contain the zero vector and hence $S$ is not a subspace.
Linear Algebra: A Modern Introduction
by Poole, David
Published by
Cengage Learning
ISBN 10:
1285463242
ISBN 13:
978-1-28546-324-7
Chapter 3 - Matrices - 3.5 Subspaces, Basis, Dimension, and Rank - Exercises 3.5 - Page 209: 7
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