Concern determinants of the following Vandermonde matrices.

Let x₁, x₂, and x₃ fixed numbers all distinct. Matrix V can be used to find an interpolating quadratic polynomial for the points (x₁, y₁), (x₂, y₂) and (x₃, y₃), where y₁, y₂ and y₃ are arbitrary. To prove the existence of an interpolating polynomial p(t) = co + c_it + c₂t² such that p(x₁) = y₁, p(x₂) = y₂ and p(x₃) = y₃.

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T 1 a b C a² b² c² V(t) = 1 1 1 1² X1 x² X2 X3 to X 13