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Linear Algebra(functionals, linear independence)

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Define linear functionals lk on Pn by
    lk(p) = p(tk)
    Show that the lk are linearly independent.


    2. Relevant equations
    q1(t)= (t-t2)(t-t3)...(t-tn)

    3. The attempt at a solution
    I really don't know where to start. I do have the following equation:
    If the lks are linearly independent then there exits as such that
    a1l1(k)+...+anln(k)=0 where all the as=0.
    That's all I have. I don't see how can I can incorporate the hint given.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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