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Homework Help: Geometrical description of a subset

  1. Feb 26, 2010 #1
    Could somebody explain to me please how to figure out a geometric description of a subspace??? I understand how to check wether the set of vectors is a subset, but how t ogive them a geometric description??

    lets say i have a subset in R3 {x: x3 = 2x1-x2}

    why the G.D. is a plane with an equation 2x1-x2-x3 = 0??

    or if I have subset {x: aTx = 0}, where a = [1;0; 0] (R3 again), the G.D is a plane yz... huh? how come? :(
     
  2. jcsd
  3. Feb 26, 2010 #2
    In the first example you just need to rearrange the set notation so that it reads:
    {x: 2x1-x2-x3 = 0}. This is a plane, just as an equation like y-x+1=0 might describe a line in R2.

    In the second case, I'm not sure what you mean by T, but I'm assuming that by aTx you just mean the vector multiplication of x by the transpose of a. In this case, note that in order to satisfy the equation, x can have non-zero y and z coordinates, but must have a zero x coordinate....ie. the equation defines the plane formed by the y and z-axes.

    Note I have used a bold font for vectors...life can get a bit confusing if you use the same notation for vectors and points!
     
  4. Feb 26, 2010 #3

    Gotcha. So i just have to look at the subset, and rearrange the equation, until it will look familiar (ie plane in 3d or a line in 2d..)

    Thanks!
     
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