These problems start with a bidiagonal n by n backward difference matrix D = I - S. Two tridiagonal second difference matrices are DDT and A = -S+21-ST. The shift S has one nonzero subdiagonal Si,i-1 1 for i = 2,..., n. A has diagonals -1,2, -1. = Show that DDT equals A except that 12 in their (1, 1) entries. Similarly DTDA except that 12 in their (n, n) entries. Note Au corresponds to -d2u/dx2 for 0 < x < 1 with fixed boundaries u(0) = 0 and u(1) = 0. DDT changes the first condition to du/dx(0) = 0 (free). DTD changes the second condition to du/dx(1) = 0 (free). Highly useful matrices.