A rod of length \(3m\) has been subjected to a distributed load \(q = -20 kN/m\) acting along its axis. Write the system of FEM equations for discretization using three finite elements of identical length. Calculate the values of the degrees of freedom, knowing that the left end of the rod has been fixed, and the right end has moved by \(0.05m\).

Assume the longitudinal stiffness \(EA = 3000\) kN. The stiffness matrix for the rod task has the form: \[ \mathbf{K} = \frac{EA}{h} [[MATH_0_BLK]] \]

The coefficients of the load vector are equal to \(P_i = \int_e \varphi_i q \, dx\). Calculate the axial force in the first element. Is this an exact or approximate result?