Question

In R^2, with the usual addition but scalar multiplication defined by a (x, y ) = (ax, y). Is R^2 vector space or not under this operation?

Answer 1

Let R be the set of all real numbers. Define scalar multiplication by

αx=α⋅x (the usual multiplication of real numbers)

and define addition by

x⊕y=max(x,y) (the maximum of two numbers)

Prove that R with these operations is NOT a vector space. Which of the eight axioms fail to hold?

Please help I know I need to prove it by using the 8 axioms but I get confused with the addition part.

Step-by-step explanation: