# Math Help - Subspace: why?

1. ## Subspace: why?

I'm sure you seen this theorem in one wording or the other that W is a subspace of V iff: 1) W is nonempty, 2) W is closed under multiplication by scalars, and 3) W is closed under vector addition.

One of the questions in the textbook asks "Explain why a subset of a vector space must be nonempty in order for it to be a subspace."

I was guessing that if W was empty, then #2 and 3 in that theorem would be disrupted since there's nothing to multiply the scalars with in #2.

What's your take on this question?