- #1
KaiserBrandon
- 54
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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.