Let V be an n-dimensional vector space with an ordered basis B. Define T:V to Fⁿ by T(x) = [x]B. Prove that T is linear.
a) T(u + v) = T(u) + T(v) and T(kv) = kT(v) for all vectors u, v, and scalar k.
b) T(u - v) = T(u) - T(v) and T(kv) = kT(v) for all vectors u, v, and scalar k.
c) T(u × v) = T(u) × T(v) and T(kv) = kT(v) for all vectors u, v, and scalar k.
d) T(u / v) = T(u) / T(v) and T(kv) = kT(v) for all vectors u, v, and scalar k.