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Calculus and Beyond Homework Help
Linear Algebra Field & Vector Space Problem
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[QUOTE="1LastTry, post: 4506229, member: 441429"] [h2]Homework Statement [/h2] Let V1 and V2 be vector spaces over the same field F. Let V = V1 X V2 = {f(v1, v2) : v1 [itex]\in[/itex] V1; v2 [itex]\in[/itex] V2}, and define addition and scalar multiplication as follows. For (v1, v2) and (u1, u2) elements of V , define (v1, v2) + (u1, u2) = (v1 + u1, v2 + u2). For (v1, v2) element of V and c [itex]\in[/itex] F, define c (v1, v2) = (c v1, c v2). a) In the definitions of addition and scalar multiplication there are three "+" and three "." To which vector space is each one associated with? b) Show that V is a vector space. NB: you must provide some reason why each of the axioms is satised. [h2]Homework Equations[/h2] To be absolute honest i have no idea what it means when it asked which vector space it belong to in part a). ANd for part 2, i do not know where to start. [h2]The Attempt at a Solution[/h2] I know that to proof fields or vector spaces, it has to satisfy with the axioms Zero vector addition scalar multiplication and etc. Just have trouble starting this problem Thanks. [/QUOTE]
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Linear Algebra Field & Vector Space Problem
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