Problem) The truss shown below is composed of five elements and four nodes as shown. A vertical load P is applied at node 4. Bar elements land 2 have axial stiffnesses of 2AE, and bars 3, 4, and 5 have axial stiffness of AE. Here, A and E represent the cross-sectional area and modulus of elasticity of a bar and we have: E = 200 GPa, A= 8e-3 m , L = 2 m , P = 20 kN The structure has 3 unknowns, which are the displacements at the 3 joints (dzy, dzy, and d4y). The stiffness matrix of the structure (K) multiplied by the unknown displacement vector (X) gives us the vector of external forces (F). To obtain the unknown displacements at joints, we want to solve the system of equations KX=F: 45 1 45 Idzy EA K= 1 0 -0.5 0 1 -0.5 -0.5 -0.5 1 X = F = dzy [day] -E) a) Solve the given system of equations to obtain the unknown nodal displacements using Cramer's rule (solve by hand). b) Solve the system using Gauss elimination method (solve by hand)