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Homework Statement
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
Homework Equations
None
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
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