1. ## Determining subspaces

An exercise in my book lists several sets of vectors, and I am to determine which sets constitutes a subspace in R^3.

According to my book, the set of all vectors on the form (a,b,0) is "not" a subspace in R^3, but I cannot understand why. The way a see it, it is closed under addition and scalar multiplication (it seems to equal the xy-plane). What am I missing? Thanks!

2. ## Re: Determining subspaces

Are there restrictions on a and b? Maybe 0 < a < b or something like that?

Nope!

4. ## Re: Determining subspaces

Maybe they just forgot to tell you. Does it contain (0,0,0)? If so, you're kind of done.

5. ## Re: Determining subspaces

If you have given the complete statement of the problem, then it is just an error in your textbook. The set of all vectors of the form (a, b, 0), where a and b can be any real numbers is a subspace of $R^3$.