For each, list three elements and then show it is a vector space.
(a) The set of linear polynomials P1 = {a0 + a1x | a0, a1 ∈ R} under the usual polynomial addition and scalar multiplication operations.
(b) The set of linear polynomials {a0 + a1x | a0 - 2a1 = 0}, under the usual polynomial addition and scalar multiplication operations.
Use Example 1.3 as a guide. Most of the ten conditions are just verifications.