Answer to Question #79218 in Linear Algebra for Ben

Question

We know that the set F(R) of functions f : R ! R, together with pointwise
addition and scalar multiplication
(f + g)(x) = f(x) + g(x) for all f; g 2 F(R) and x 2 R
(
f)(x) = f(x) for all f 2 F(R),  2 R and x 2 R:
In this problem, you are asked to discuss whether F(R) continues to be a vector space
when the operations (+;
) are replaced by other addition/scalar multiplication opera-