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!

Vectors, linear algebra

  1. Jan 19, 2009 #1
    given the vectors,

    show that if v1,v2......vk+1. are dependant then v1,v2......vk+1 are definitely dependant.

    can i say that in a series of dependant vectors, at least one must be a linear combination of the others therefore, if v1,v2......vk+1 are dependant, v1,v2......vk+1 must be since it contains the vector which was a linear combination (from the larger series)
  2. jcsd
  3. Jan 19, 2009 #2


    User Avatar
    Gold Member

    What is definitely dependant?
  4. Jan 19, 2009 #3


    Staff: Mentor

    I think you have written the problem incorrectly. My guess is that this is the problem:

    Given the vectors, v1,v2,...,vk+1,
    show that if v1,v2,...,vk+1 are linearly dependent, then v1,v2,...,vk are linearly dependent.

    To answer your question, yes, in any collection of linearly dependent vectors, it must be the case that one of them is some linear combination of the rest.
  5. Jan 20, 2009 #4
    Huh? In R^2 the vectors (1,0), (0,1), (1,1) are linearly dependent, but (1,0) and (0,1) are linearly independent.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Vectors, linear algebra