Linear Subspace of R^n: Arithmetic Progressions Verification

[KaiserBrandon]

Homework Statement

Is the set of all vectors in R^n whose components form an arithmetic progression a linear subspace of R^n?

Homework Equations

none

The Attempt at a Solution

I basically need one thing verified: would (0,0,0,...,0) be considered an arithmetic progression. The definition says that an arithmetic progression is one where the difference between any two consecutive members of the sequence is constant. Since 0-0=0, it would seem like it is an arithmetic sequence, however, is there a condition that the difference must be non-zero? If not, then (1,1,...,1), (2,2,...,2), etc. would all be arithmetic progressions, and that doesn't seem right to me.

 

[Dick]

No, I don't think there's any condition on an arithmetic sequence saying the difference can't be zero.

 

[KaiserBrandon]

alright, so in that case it is a linear subspace since it meets the three requirements to be a linear subspace. Thanks.