Subspaces Proposition If U is closed under and.,then U equipped with the restrictions of+ and.satisifies the 8 vector space axioms Al,A2,A3,A4 and S1,S2, S3,S4.Hence (U,+,is a vector space.U is said to be a subspace of V Examples (1)The zy-plane CR3. (2)The space of polynomial functions of one variable of degree n Poln(R)∈FR(R) 4口+心左4生主9QGSubspaces Proposition If U is closed under + and •, then U equipped with the restrictions of + and • satisifies the 8 vector space axioms A1, A2, A3, A4 and S1, S2, S3, S4. Hence (U, +, •) is a vector space. U is said to be a subspace of V . Examples (1) The xy-plane ⊂ R 3 . (2) The space of polynomial functions of one variable of degree n Poln(R) ∈ FR (R)