For each of the following sets, determine whether it is a vector space over the given finite field, fq. if it is a vector space, determine the number of distinct bases it can have.
a. q = 2,S= {(a,b,c,d,e) : a+b+c+d+e=1}
b. q =3,T={x,y,z,w) : xyzw=0}
c. q = 5, U={(λ+μ,2μ,3λ + v,v) : λ,μ,v F5}
d. q prime, V= {(x₁,x₂,x₃) : x₁=x₂-x₃}