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Question

Evaluate the determinant, in which the entries are functions. Determinants of this type occur when changes of variables are made in calculus.

3x23y211\left|\begin{array}{cc}{3 x^{2}} & {-3 y^{2}} \\ {1} & {1}\end{array}\right|

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We need to compute the determinant of the matrix

3x23y211\begin{vmatrix} 3x^{2}&-3y^{2}\\ 1&1 \end{vmatrix}

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