Consider the heat equation Ut = Uxx with the initial and boundary conditions u(x,0) = f(x), u(0, t) = 1, u(1, t) = 2. Divide the interval [0, 1] into N+1 grid points xi = = ih, for i = 0, . .., N+1, with grid spacing h = N+1· Let u? denote the approximate solution to this problem at (ï¿, tn). Using the approximations 1 n u i-1 - 2 + Uxx (xi, tn) ≈ h² n+1 _ un k this system can be written as un+1 = Au + b where A is a an Nx N matrix, u = (un,….,un)¹ and 6 are N-dimensional columns vectors. Write down expressions for A and 6 for N = 5. You can leave your answers in terms of h and k. Ա ut (xi, tn) ≈ U i