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 with a basic linear algebra proof

  1. Feb 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Let x and y be nonzero vectors in Rn. Prove ||x+y|| = ||x|| + ||y|| if and only if y = cx for some c > 0.

    2. Relevant equations

    Formula for vector magnitude, basic properties of vectors, possibly other vector formulas

    3. The attempt at a solution

    I have proved the first part, that is, that ||x+y|| = ||x|| + ||y|| if y=cx for some c > 0.

    Now I have to prove the second part:
    If ||x+y|| = ||x|| + ||y|| there is some c > 0 such that y = cx.

    I don't know how to begin proving this. I'm guessing I need to find c using the equation. However I can't think of a method that allows me to do this.

    If someone could give me hint or help me get started, I would greatly appreciate it. Thanks.
     
  2. jcsd
  3. Feb 12, 2009 #2

    Mark44

    Staff: Mentor

    Isn't ||x + y||^2 = (x + y) . (x + y)?
     
  4. Feb 12, 2009 #3
    Thank you, that was enough for me to figure it out :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help with a basic linear algebra proof
Loading...