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) .

Answer 1

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

Answer 2

How?

Answer 3

i forget
what are the axioms?

Answer 4

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

Answer 5

also the zero is in there

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

or would that be considered evaluating it at -1