@Kitonum Thank you very much! Worked perfectly

@vv  Thanks for your reply!

You see, first equation has n^2 unknowns, second one has the same n^2 unknowns, and I have n^2 equations. That's why I think the system should be solvable fine after the linearization. 

Is my reasoning correct? 

EDIT: I just realized that my question said `N unknowns and N equations`. It was a mistake! Sorry for that, it was very late when I wrote that.