For certain functions f(x, y), g(x, y), p(u, v), q(u, v) it is known that f(x0, y0) = u0, g(x0, y0) = v0 and that fx(x0, y0) = 2, fy(x0, y0) = 3, gx(x0, y0) = −1, gy(x0, y0) = 5, Pu(u0, v0) = 7, pv(u0, v0) = 1, qu(u0, v0) = −3, qv(u0, v0) = 2. Let z = F(x, y) = P(f(x, y), g(x, y)), w = G(x, y) = q(f(x, y), g(x, y)) and find the Jacobian matrix of z(x, y), w(x, y) at (x0, y0).
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