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!

Homework Help: Orthogonal complement question

  1. Apr 24, 2006 #1
    I have the set

    s = span ( [[0][1][-1][1]]^{T} )

    And I need to find the orthogonal complement of the set.

    It seems like it should be straight foward, but I'm a bit confused. I know that S is a subspace of R^4, and that there should be three free vairables.

    What I did so far is to take the column vector given, and I need to find the null space of its transpose. The three free variables I picked are [tex]x_1= s, x_2=t, x_3=w, x_4=t-w[/tex].

    However, x_1=s is throwing me off because its always zero. I guess what I'm really asking is, what exactly is the solution space of the homogenous system,
    in this problem?

    Last edited: Apr 24, 2006
  2. jcsd
  3. Apr 24, 2006 #2


    User Avatar
    Science Advisor

    You row reduce it (actually it is already row reduced) and you get 3 free variables: x1, x3, and x4. You have a pivot for x2. Your equations will be
    x1 = x1
    x2 = (an expression involving some of x1, x2, x3)
    x3 = x3
    x4 = x4
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook