(1) Consider the one-dimensional Poisson equation: -u" (x) = f(x) Vx € [0,1], (1) (2) u(0) = u(1)=0 where f is a given function and u is the solution. In class, we used a piecewise linear finite element (FE) discretization with N-1 equally spaced mesh points to approximate u. We noticed that the FE discretization reduces the Poisson equation (1)-(2) to the following linear system: Ax=b, where A is an (N-1) x (N-1) matrix and b is an (N-1) vector. (a) Find all the entries in the matrix A for N = 4. (b) Find all the entries in the matrix A for a general N. (3)