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LinAlg - Due today! (Linear independence)

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A=[-2
    -7
    -1]

    B=[-2
    -4
    -3]

    C=[0
    6
    -4]

    Determine whether or not the three vectors listed above are linearly independent or linearly dependent.
    I have determined that they are linearly DEPENDENT.

    If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.


    2. Relevant equations
    none, sorry

    3. The attempt at a solution
    I have put the vectors into a matrix and solved it... but then I got something strange, and everytime I do it... I always get different answers. I have determined that they are linearly dependent though.
     
  2. jcsd
  3. Nov 22, 2008 #2
    please help... I have no idea what to do =(
     
  4. Nov 22, 2008 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You want to solve aA+bB+cC=0. If you equate the components you get three equations in the three unknowns. The first one is -2a-2b=0. What are the others? If you know they are linearly dependent you should expect to get lots of solutions. Your first one says a=-b. I would substitute that into the other equations.
     
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