Thread: 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

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

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.