And in general how can I show wether a subset of a vector space is affine or not?

Thank you!

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- November 19th 2011, 09:54 AMgotmejerryAre this an affine subset of R^n?

And in general how can I show wether a subset of a vector space is affine or not?

Thank you!

- November 19th 2011, 12:07 PMHallsofIvyRe: Are this an affine subset of R^n?
A subset S, of vector space V, is an "affine" set if and only if for a member of S, the set is a sub

**space**of V. - November 20th 2011, 04:21 AMgotmejerryRe: Are this an affine subset of R^n?
What is your X here?

- November 20th 2011, 05:19 AMHallsofIvyRe: Are this an affine subset of R^n?
Whatever the overall space is. In your problem, it would be . As long as you are working in you can charactize an "affine set" (that is not a subspace), geometrically, as a line or plane or "hyper-plane" (of whatever dimension) that does NOT include the origin. The condition that simply says that this is the set of all vectors in with length . Is that a plane (of whatever dimension) in ?

- November 20th 2011, 06:30 AMgotmejerryRe: Are this an affine subset of R^n?
Hmm, yes I tihnk that is a plane. By the way I found an other way of solution but Im not sure wether it is right or not. So is affine if for all and .

And what I did:

then follows

and because and

So it is an affine set. - November 21st 2011, 04:51 PMalbiRe: Are this an affine subset of R^n?
You should have: