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What can we say about this matrix?

Let $$V = \left\{ f : [0,1] \to \mathbb R\ :\ f \text{ is a polynomial of degree} \leq n \right\}$$ Let $f_j(x)=x^j$ for $0 \le j \le n$ and let $A$ be the $(n+1) \times (n+1)$ matrix given by $$...
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