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Linear subspace of R^n

  1. Nov 8, 2009 #1
    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. jcsd
  3. Nov 8, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    No, I don't think there's any condition on an arithmetic sequence saying the difference can't be zero.
     
  4. Nov 8, 2009 #3
    alright, so in that case it is a linear subspace since it meets the three requirements to be a linear subspace. Thanks.
     
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