1. Not finding help here? Sign up for a free 30min 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!

Help proving a subset is a subspace

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that the set of all 3-vectors orthogonal to [1, -1, 4] forms a subspace of R^3.

    2. Relevant equations

    Orthogonal means dot product is 0.

    3. The attempt at a solution

    I know the vectors in this subspace are of the form
    [a,b,c] where a - b + 4c = 0.
    However I don't know how to use this to show there is closure under vector addition and scalar multiplication.
     
  2. jcsd
  3. Apr 16, 2009 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    Let v_1 and v_2 be two vectors orthogonal to the given vector (call it a), i.e.

    [tex] v_1 \cdot a = 0 [/tex]
    [tex] v_2 \cdot a = 0 [/tex]

    Now, using these, all you have to do is show that

    [tex] (v_1 + v_2) \cdot a = 0[/tex]

    HINT: Use distributivity of the dot product.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help proving a subset is a subspace
  1. Subspace and subset (Replies: 10)

  2. Subset and subspace (Replies: 4)

  3. Subset and subspace (Replies: 1)

Loading...