Logarithm 11

Calculus Level 3

\[\begin{align} f(x,y,z) & = \frac{\ln(y^x)}{z} \\ g(x,y) & = e^{- x^2 - y^2} \\ A & =
\begin{bmatrix} g(0,1) & f(0,3,5) & g(0,-1) \\ f(4,e,2) & g(0,0) & f(3,e^3,3) \\ g(1,0) & f(7,1,1) & g(-1,0) \\ \end{bmatrix} \end{align} \]

Given the functions \(f\) and \(g\) and matrix \(A\) above, find the determinant of \(A\).

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