# subspaces

• Jan 16th 2009, 08:09 AM
CarmineCortez
subspaces
Give an example of a nonempty subset of U of R^2 st U is closed under scalar multiplication but U is not a subspace of R^2.

so its ovbiously open under addition, so if I add another vertor in R^2, U+v will not be in R^2.

not sure what this would be.
• Jan 16th 2009, 08:15 AM
HallsofIvy
Quote:

Originally Posted by CarmineCortez
Give an example of a nonempty subset of U of R^2 st U is closed under scalar multiplication but U is not a subspace of R^2.

so its ovbiously open under addition, so if I add another vertor in R^2, U+v will not be in R^2.

not sure what this would be.

"U+v" makes no sense until you have specified what U is- and that's what the problem asks you to do!

Let A be the subspace spanned by <1, 0> and B the subspace spanned by <0, 1>. What is the union of those two subspaces? Can you prove that \$\displaystyle U= A\cup B\$ is closed under scalar multiplication but NOT under addition?
• Jan 16th 2009, 08:56 AM
CarmineCortez
subspaces and spans
U is a subspace of the set of all polynomials P, it contains all polynomials of the form p=az^2+bz^2. Find the subspace W of P st P = U+W

U+W is the span of P, not sure how to represent it.

I meant to make a new thread.
• Jan 16th 2009, 11:17 AM
HallsofIvy
Quote:

Originally Posted by CarmineCortez
U is a subspace of the set of all polynomials P, it contains all polynomials of the form p=az^2+bz^2. Find the subspace W of P st P = U+W

U+W is the span of P, not sure how to represent it.

I meant to make a new thread.

Are you sure about "p= az^2+ bz^2"? That is no different from "all polynomials of the form p= az^2".
(And is not a subspace- it does not contain the 0 "vector". You probably meant "all polynomials of the form p= az^2+ bz+ c".)