Okay, so I'm having some trouble with this topic. If a question asks you to show that a set is a subspace (or not a subspace), do you show the following:

The set is not empty

The set is closed under vector addition, i.e.

The set is closed under scalar multiplication, i.e.

1) Show that the set

is not a subspace of

Would I do the following:

Therefore, it does not contain the vector, hence not a subspace in