1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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..)

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Geometrical description subset Date
Geometric description of the nullspace Nov 8, 2009
Geometric description homework Mar 16, 2009
Geometric description of kernel Nov 13, 2007
Geometric description of a kernel Nov 11, 2007
Linear Algebra: Geometric Description of Span Aug 25, 2007