For each of the following subsets of the indicated vector space V , decide whether it is a subspace.
1. GLn(F) in V = Mn(F).2. The set Symn ⊆ V = Mn(F) of symmetric matrices: Symn = {A ∈ Mn(F) | AT = A}.
3. For fixed A ∈ V = Mn(F), the centralizer of A C(A) = {B ∈ Mn(F) | AB = BA}.
4. The set of all functions f ∈ V = C(R) for which f(1) ∈ Q.
I missed this class and am not really sure how to determine if something is a subspace so I'm trying to do some practice. Any help would be great.