Vector Space Proof: A Complete Solution to α*f(-2) + β*f(5) = 0

Abukadu
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Hi, good morning!

I'm having trouble with vector space.

Let there be α and β some given numbers. Prove that the set of all the real numbers f(x) so that: α*f(-2) + β*f(5) = 0 is a vector space !

Could someone please write a full solution for he axiom scalar multiplication?
 
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There is no "Axiom scalar multiplication"

You want to show that scalar multiplication as it is defined on your "Vector Space" has a multiplicative identity, and that distributivity holds with the operation of vector addition defined on your vector space.

So how is it defined on this Vector Space?
 

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