SOLUTION: You have a given set, of all polynomials of the form p(t) = a + t^2, where a is in R (reals). How do you determine whether that given set is a subspace of P(sub n) for an approp

Algebra ->  Subset -> SOLUTION: You have a given set, of all polynomials of the form p(t) = a + t^2, where a is in R (reals). How do you determine whether that given set is a subspace of P(sub n) for an approp      Log On


   

Question 4399: You have a given set, of all polynomials of the form p(t) = a + t^2, where
a is in R (reals). How do you determine whether that given set is a subspace
of P(sub n) for an appropriate value of n?
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
For a given vector space V, a subset W is a subspace of V if and only
if av+bw is in W for all v, w in W and scalars a,b.(reals here)

Now W = {a + t^2| a is real} = set of polynomials in R with
deg <=2 and the coefficient of t^2 = 1, the coefficient of t = 0.
Clearly, W is a subset of P2 = {a + bt + ct^2| a,b,c are reals}
= set of polynomials in R of degree <=2.
But, W is not a subspace of P2.
Since t^2 is in W but t^2 + t^2 = 2t^2 is not in W.

Kenny