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## Homework Statement

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.

## Homework Equations

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.

## The Attempt at a Solution

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.