1. The problem statement, all variables and given/known data the set R^(2) with the usual vector addition forms an abelian group. For a belongs to R and x=(x1,x2) belongs to R^(2) we put a *x :=(ax1,0),this defines a scalar multiplication R*R^2 ---R^2 (a,x)---a*x. determine which of the axioms defining a vector space hold for the abelian group R^2 with the scalar multiplication 2. Relevant equations 3. The attempt at a solution I know that a*x1=ax1 but a*x2=0?? It confused me . And how to use an axiom to define it ?