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Determinantsmedium
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The Vandermonde determinant formula states that det⁡(1x1x121x2x221x3x32)=(x2−x1)(x3−x1)(x3−x2)\det\begin{pmatrix} 1 & x_1 & x_1^2 \\ 1 & x_2 & x_2^2 \\ 1 & x_3 & x_3^2 \end{pmatrix} = (x_2 - x_1)(x_3 - x_1)(x_3 - x_2)det​111​x1​x2​x3​​x12​x22​x32​​​=(x2​−x1​)(x3​−x1​)(x3​−x2​) Using this formula, what is det⁡(1241391525)\det\begin{pmatrix} 1 & 2 & 4 \\ 1 & 3 & 9 \\ 1 & 5 & 25 \end{pmatrix}det​111​235​4925​​?