Properties of the Determinant II

Algebra Level 3

Some matricies, like the Vandermonde matrix, have a determinant with a cute factorisation.

If \(\begin{vmatrix} 1 & a_1 & a_1^2 \\ 1 & a_2 & a_2^2 \\ 1 & a_3 & a_3^2\end{vmatrix} \neq 0\), what can we say about \(a_1\),\(a_2\), and \(a_3\)?

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