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ak123456
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Homework Statement
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
Homework Equations
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 ?