Problem 1. A 5 x 5 square grid in the plane has a 3 x 3 interior grid of interior points: 9 unknowns. Create
the 9 x 9 matrix K (symmetric and definite) for Laplace: diagonal is all 4, most rows have less than four 1's.
Use [L, U] = lu (K) to find the triangular factors L and K. Use spy(L+U_ to see when those matrices have
nonzero entries. Display K, L, U, and the output from spy (L+U).
Additional problems (file attached):
Section 3.6: 10, 11, 18
Section 4.1: 3, 5, 6