zero vector subspace

Question

Does a zero vector by itself constitute a subspace? It appears to satisfy all 3 conditions.

1. Contains zero
2. Hold under addition
3. Holds under scalar multiplication

Can any other single vector do that?

Answer 1

Yes, it is called the trivial vector space. No other vector can do that because any vector space must have a zero vector. (so if it contains only one vector then it must be the zero vector)