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Linear Algebra Geometric Planes

  1. Sep 5, 2011 #1
    For a homogeneous system of 3 equations in 3 unknowns (geometrically
    this is 3 planes in space all containing the origin) describe the relationship between
    the (three) geometric possibilities for the solution set and the number of free variables (non
    pivots) in RREF(A) where A is the coefficient matrix.

    I understand what RREF stands for. However, I don't understand how to approach the question or what it is asking
     
  2. jcsd
  3. Sep 5, 2011 #2

    HallsofIvy

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    Staff Emeritus
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    Obviously, three planes all passing through the origin have the origin in common. It is possible that the origin is the only point in common. But it is also true that there is a whole line through the origin lying in all three plane, or an entire plane in all three planes. Try drawing pictures to see what the geometric relationships would be and what effect they would have on the RREF matrix.
     
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