Consider the equation Uxx + Uyy + Ux = = f 1 = = 0,..., N + 1. Let ui,j on the unit square with u = 0 on the boundary. Let (x,y) denote the point whose coordinates are x₁ = ih and yj = jh, where h N+₁, and i 0,..., N + 1 and j denote the approximate solution at (x, yj). Using the approximations N+1' 4ui, j Uxx (xi, Yj) + Uyy (Xi, Yj) ≈ Ui−1,j + Ui+1,j + Uį,j+1 + Ui,j—1 h² and Ux x (2i,j) ~ Ui+1, j - Ui - 1,j 2h this system can be written as the linear system A☛ = 6, where A is an N² × N² matrix, and and 6 are N² dimensional column vectors. Write down A for N = 3. You can leave you answer in terms of h.