Problem 1 [1 pt] Let U, V be vector spaces. Let W be the set of pairs (u, v) where u E U and v E V. Define (u, v) + (u', v') = (u + u', v + v'). For a real number c, define c(u, v) = (cu, cv). W is a vector space; show that it satisfies some axioms: choose 2 additive, 2 multiplicative and 1 distributive axioms, and show that W satisfies them. Recall that a subset W of a vector space V is a subspace of V if it contains 0 and is closed under addition and scalar product