Question: Answer using FEM and use stiffness matrix like K [ 4 x 4 marrix ] - Pcr [ another 4 x 4 Matrix ] *

Answer using FEM and use stiffness matrix like K[4x4 marrix]- Pcr [another 4x4 Matrix]*q =0 you convert q to golbal vector somehow by adding the 2 marixes to two global bigger matrix Also, u were to assume this is 1d euler-Bernolli beam element (AKA only vertical and theta 2 DOF in each node not 3)
Answer using FEM and use stiffness matrix like K

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