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Linear algebra proof

  1. Feb 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Let a1, a2, ..., an live in R. Prove that the equation

    det [ A ] = 0

    where A:
    1 x x^2 ... x^n
    1 a1 a1^2 ... a1^n
    1 a2 a2^2 ... a2^n
    . . . . .
    . . . . .
    . . . . .
    1 an an^2 ... an^n

    has exactly n solutions if and only if the a1, ..., an are distinct; i.e. ai=/=aj for all i=/=j

    2. Relevant equations

    3. The attempt at a solution
    Well, my problem is that I don't even know where to really start. So my attempts at a solution don't exactly make much sense. I was just playing around hoping I would come up with something, which I didn't
    Last edited: Feb 23, 2010
  2. jcsd
  3. Feb 24, 2010 #2
    What property of a matrix [tex]A[/tex] ensures that its determinant is zero (or, inversely, not zero)? How does this property connect to the relationships between the rows (or columns) of [tex]A[/tex]?
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