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Conditions on overdetermined linear system to be consistent?

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    An overtdetermined system - If m > n, then the linear system Ax = b is inconsistent for at least one vector b in ℝ^n.

    3. The attempt at a solution

    If m > n (more rows than columns), in which case the column vectors of A cannot span ℝ^m (fewer vectors than the dimension of ℝ^m).

    So, there is at least one vector b in ℝ^m that is not in the column space of A, and for that b the system A x = b is inconsistent by Theorem 4.7.1 which states A system of linear equations  is consistent if and only if b is in the column space of A.


    [STRIKE]So the conditions that must be imposed on b must be to zero out variables? I know this is wrong but I don't really know what to do?[/STRIKE]

    ******************UPDATE******************



    I think I solved it guys, can someone check my solution and tell if its correct if not, what do I need to do to make it correct. I've attached the solution to this poste. Thanks.









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    Attached Files:

    Last edited: Apr 16, 2012
  2. jcsd
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