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Homework Help: Vector subspace

  1. Dec 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Can you help please? I have this problem:
    Let S be the set of all vectors parallel to the hyper-plane 4x +2y+z + 3r =0 in R^4 .
    (a) Show that S is a subspace, (b) Determine a basis for S , (c) Find its dimension

    2. Relevant equations

    3. The attempt at a solution
    S= { u=(x, y,z,r) | 4x+2y+z+3r=0} u is in R^4.
  2. jcsd
  3. Dec 28, 2015 #2


    Staff: Mentor

    That won't work. If the vectors in S are parallel to the hyperplane, then all of these vectors are perpendicular to a normal to the hyperplane. If you're given the equation of a hyperplane, do you know how to find a normal to this hyperplane?
  4. Dec 29, 2015 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If u is a vector and S is a hyperplane, what does it mean to say that u is parallel to S? You will need a definition of "parallel" to answer that.
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