For each of the following subsets of the indicated vector spaceV, decide whether it is a subspace.

1. GL2. The set Symn(F) inV=Mn(F).n ⊆ V=Mn(F) ofsymmetricmatrices: Symn={A ∈ Mn(F)| AT=A}.

3. For fixedA ∈ V=Mn(F), thecentralizerofA C(A) ={B ∈ Mn(F)| AB=BA}.

4. The set of all functionsf ∈ V=C(R) for whichf(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.