Firstly, I need an answer for 1. and then please make the others. Lesson is numeral solution to partial differentials equations

Problem 5.4 (stiffness and mass matrix). Consider the Helmholtz equation Au+ku=0 in St, on . (5.47) u = g 1. Show that from the discretized variational formulation: Find u V such that VE Vh -(u', v') + k (u, v) = (f, v) where V = span{,...,n} V, one obtains the linear system -Ku+k Mu= b, where K is the stiffness matrix and M is the mass matrix and b contains the Dirichlet boundary conditions. 2. Discuss the existence and uniqueness of a solution to the above variational prob- lem. 3. Assume that a triangulation of the domain element with nodes (T, y1), (2, 2), (3, matrices using Maple. is given. Compute on a triangular 3) the element stiffness and mass Problem 5.4 (stiffness and mass matrix). Consider the Helmholtz equation Au+ku=0 in St, on . (5.47) u = g 1. Show that from the discretized variational formulation: Find u V such that VE Vh -(u', v') + k (u, v) = (f, v) where V = span{,...,n} V, one obtains the linear system -Ku+k Mu= b, where K is the stiffness matrix and M is the mass matrix and b contains the Dirichlet boundary conditions. 2. Discuss the existence and uniqueness of a solution to the above variational prob- lem. 3. Assume that a triangulation of the domain element with nodes (T, y1), (2, 2), (3, matrices using Maple. is given. Compute on a triangular 3) the element stiffness and mass