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Linear Algebra and matrices

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data

    The following system of linear equations has infinitely many solutions.
    {xi + xi+1 + xi+2 = 0 : 1 < i < 7}

    3. The attempt at a solution
    I feel like I have the capacity to solve this problem however I can't interpret what the question is even asking with all the i's in it.
    If someone could just interpret the question for me that would be very helpful.
     
  2. jcsd
  3. Jan 31, 2010 #2

    HallsofIvy

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    Be careful with your notation. I would interpret x_(i+1) as [itex]x_{i+1}[/itex] but I would interpret xi+1 as [itex]x_i+ 1[/itex]. That confused me for a moment!

    If your problem is [itex]\{x_i+ x_{i+1}+ x_{i+2}= 0: 1< i< 7\}[/itex], then you have 7 equations in 9 unknown values.

    [itex]x_1+ x_2+ x_3= 0[/itex]
    [itex]x_2+ x_3+ x_4= 0[/itex]
    [itex]x_3+ x_4+ x_5= 0[/itex]
    [itex]x_4+ x_5+ x_6= 0[/itex]
    [itex]x_5+ x_6+ x_7= 0[/itex]
    [itex]x_6+ x_7+ x_8= 0[/itex]
    [itex]x_7+ x_8+ x_9= 0[/itex]
     
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