1. The problem statement, all variables and given/known data [Dx De ; 0 0 ].[ U ; V ] = [ 0 0 ] U : Nx1 vector V : a scalar Dx : NxN matrice ( dL / dx ) De : Nx1 vector ( dL / dE ) L is set of equations ( N amount ) E is a parameter in equations x is unknowns ( N amount ) I need to derive U and V ( tangent vector components ) to apply pseudo-arclenght method to solve set of equations I need to find a supplementary equation in form of U(X-Xo) + V(E-Eo) - S = 0 S is the arclength step size 2. Relevant equations Is it derivable by hand or do i need a algorithm to find U and V ? 3. The attempt at a solution if i set V scalar as 1 U = inv(Dx)(-De) i can deduce U components but if V is zero then i cant find N-dimensional vector , I heard that it can be done with triangulation and complete pivoting. How could it be possible?