# Thread: Bases in Linear Algebra - Midterm Tomorrow!

1. ## Bases in Linear Algebra - Midterm Tomorrow!

Hey quick question thats been bugging me. Suppose I have a vector space V and a basis B that describes it. B is a subspace of V right?

I figure it is because for B to be a basis it must be a span and be linearly independent. Both spans and linear independent sets are described as subsets in my book. However, bases aren't. Any ideas?

2. Let's say we're talking about a vector space. The basis is a set of linear independent vectors, that through linear combinations span(V). I think the basis itself though is just this set of vectors, not the coefficients as well. For this reason I believe the basis is a subset of vector space V, not a subspace.