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Spanning set of U={w€R3|w(dot)(3,-2,1)=0}

  1. Sep 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Basically im trying to find a spanning set for the plane through the origin with a normal of
    (3,-2,1) that is an element of R3

    "Let u = (3, 2, 1), and U ={wεR|w*u=0}"
    Find a spanning set for U


    2. The attempt at a solution

    Just guessing blindly here:

    (3,-2,1)=3(1,0,0)-2(0,1,0)+1(0,0,1)
    we were taught to say (1,0,0)=e1, (0,1,0)=e2, and (0,0,1)=e3 so:

    3e1-2e2+e3 would be a linear combination of this vector (?)

    then if I let:
    v=(x,y,z)=x(1,0,0)+y(0,1,0)+z(0,0,1)

    u(dot)v=3xe1-2ye2+ze3=0

    so does U=span{3xe1,-2ye2,ze3} ? I just don't know how to account for the fact that they equal 0 in the span.

    Thank you to anyone who can help!
     
  2. jcsd
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