Solve the Problem $\mathrm { H }$ Be the Set of All Points of the Form

Multiple Choice

Solve the problem.
-Let $\mathrm { H }$ be the set of all points of the form $( \mathrm { s } , \mathrm { s } - 1 )$ . Determine whether $\mathrm { H }$ is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy.
A: Contains zero vector
B: Closed under vector addition
C: Closed under multiplication by scalars

A) $\mathrm { H }$ is not a vector space; fails to satisfy all three properties
B) $\mathrm { H }$ is not a vector space; does not contain zero vector
C) $\mathrm { H }$ is not a vector space; not closed under vector addition
D) $\mathrm { H }$ is a vector space.