Answer
See below
Work Step by Step
Assume that $x$ be the vector in $S$
We can write set $S$ as $S=\{(x,y,z) \in R^4:x+y+z=1\}$
Since $(0,0,0) \notin S$, $S$ is not a subspace of $R^3$
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 4 - Vector Spaces - 4.3 Subspaces - Problems - Page 273: 6
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