# Vector Subspaces

• Mar 10th 2007, 11:43 AM
Ranger SVO
Vector Subspaces
Its Spring Break so I've decided to get and stay caught up

Determine if the given set is a subspace of Pn, for an appropriate value of n

1. All polynomials of the form p(t) = at^2, where a is in R

2. All Polynomials of the form p(t) = a + t^2, where a is in R

As always an explination is much more important than an answer.

Thanks
• Mar 10th 2007, 02:34 PM
topsquark
Quote:

Originally Posted by Ranger SVO
Its Spring Break so I've decided to get and stay caught up

Determine if the given set is a subspace of Pn, for an appropriate value of n

2. All Polynomials of the form p(t) = a + t^2, where a is in R

I don't remember all the properties of a space, but 2) fails because the sum of two elements is not an element:
(a + t^2) + (b + t^2) = (a + b) + 2t^2
which is not an element of {a + t^2}.

-Dan
• Mar 10th 2007, 03:51 PM
ThePerfectHacker
Quote:

Originally Posted by Ranger SVO

1. All polynomials of the form p(t) = at^2, where a is in R

Yes.

1)k(at^2)=(ka)t^2

2)at^2+bt^2=(a+b)t^2

Vector subspace.