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: Subspaces and Basis

  1. Nov 8, 2008 #1
    1. The problem statement, all variables and given/known data

    Let u be a vector where u = [4 3 1]. Let A be the set of all vectors orthogonal to u. Show that A is subspace of R^3. Then find the basis for A.

    2. Relevant equations

    3. The attempt at a solution

    For showing that A is a subspace...

    Zero vector is in A because A(0) = 0

    For any u & v, u+v is in A because Au=0, Av=0, and A(u+v) = Au+Av = 0

    And for any scalar c, A(cu) = c(Au) = c(o) = 0

    As for the basis, I really have no idea where to even start with that.

    Thanks for any help.
  2. jcsd
  3. Nov 8, 2008 #2


    Staff: Mentor

    You should do the first part of this problem; namely, finding the set of vectors that are orthogonal to u = (4, 3, 1). How can you tell that an arbitrary vector (x, y, z) is orthogonal to a given vector?
    None of this makes any sense. A is a set, not a matrix, so it doesn't make any sense to multiply a vector by A.

    As for finding a basis for A, if you do the first part you will be on your way toward a basis.
  4. Nov 9, 2008 #3
    I'm not entirely sure how to show an arbitrary vector is orthogonal to a given vector. I've looked through my text for help, but it's not really helping.
  5. Nov 9, 2008 #4


    Staff: Mentor

    Is "dot product" a hint?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook