Verify that there exists a function g: R²->R² such that

Last updated: 7/24/2022

Verify that there exists a function g: R²->R² such that u = (u, v) = g(x) for the system 5xu²+ 3yv^4 = 8 2xy(u² - v²) = 0 near the point (1,1,-1,-1) by calculating det(D(u, v)F(1, 1,-1,-1)) where F: R^4->R² is a C¹ function satisfying F(1, 1,-1,-1) = 0