Consider P(F) as the set of all the polynomials f (x) of degree less than 4 such that
f (1) = 0 . Show that P(F) is a subspace of P4 (X ). Also find the dimension of P(F) .

Question

Consider P(F) as the set of all the polynomials f (x) of degree less than 4 such that 
f (1) = 0 . Show that P(F) is a subspace of  P4 (X ). Also find the dimension of P(F) .

anonymous · Answer

this is an exercise in what you have to check that one set is a subspace of another

anonymous · Answer

How?

anonymous · Answer

i forget 
what are the axioms?

anonymous · Answer

gotta be close right? $$f+g\in S$$ i.e. 
$$(f+g)(1)=0$$ 
that you can do

anonymous · Answer

also the zero is in there

anonymous · Answer

How do I prove that it is closed under addition and scalar multiplication

anonymous · Answer

add to of them and see that when you evaluate the sum at 1 you still get 0

anonymous · Answer

so could I add x+(-x^2)

anonymous · Answer

or would that be considered evaluating it at -1