Results 1 to 2 of 2

Math Help - Linear Independence/Dependence

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    16

    Linear Independence/Dependence

    Determine whether the given vectors are linearly independent or dependent. If the vectors are dependent, find a dependency relationship.

    [(1,-1,2,3), (2,-1,1,-1), (-1,1,1,1)]

    I know what to do if I have 4 vectors in R4, but with three I can't take a determinant and so I'm kinda lost. Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853
    Use the definition of "independence"?

    Are there numbers, a, b, c, not all 0, such that
    a(1, -1, 2, 3)+ b(2, -1, 1,-1)+ c(-1, 1, 1, 1)= (0, 0, 0, 0)?

    If not they are independent. If there are such numbers the vectors are dependent and the equation with those a, b, c is the "dependency relationship".

    That is the same as solving the four equations a+ 2b- c= 0, -a- b+ c= 0, 2a+ b+ c= 0, 3a- b+ c= 0. a= b= c= 0 is an obvious solution. Is it the only solution?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linear dependence/independence
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 7th 2010, 07:18 PM
  2. Linear dependence/independence
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: July 27th 2010, 09:34 AM
  3. Linear Dependence/Independence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2010, 02:12 PM
  4. Linear Dependence & independence
    Posted in the Advanced Algebra Forum
    Replies: 11
    Last Post: March 20th 2009, 03:39 AM
  5. Linear dependence and independence
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 3rd 2008, 12:51 AM

Search Tags


/mathhelpforum @mathhelpforum