MATB24H3 Final: Lecture2.pdf
Document Summary
In addition, the following properties must be satis ed: For all v, u, w v and all r, s f, A1. v (u w) = (v u) w) (associativity of addition), A2. v u = u v (commutativity of addition), Z v such that z x = x for all x v (existance of additive identity), For each x v x v such that x x = z (existance of additive inverse for each element of v), S1. r (v u) = (r v) (r u) (distributive law), S2. (r + s) v = (r v) (s v) (distributive law), S3. r (s v) = (r s) v (associative law), S4. e x = x for all x v (preservation of scale). Addition and multiplication in z3 is as de ned in the previous lecture. Show that m2x2(cid:2)z3(cid:3), , is a vector space over z3. c2 d2(cid:21) m2x2(cid:2)z3(cid:3),, then solution.
