# Linear subspace of R^n

1. Nov 8, 2009

### KaiserBrandon

1. The problem statement, all variables and given/known data

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

2. Relevant equations

none

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 8, 2009

### Dick

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

3. Nov 8, 2009

### KaiserBrandon

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