(a) Find the L U factorization of the n × n tridiagonal matrix An with all 2's along the diagonal and all - 1's along the sub- and super-diagonals for n = 3, 4 and 5.
(b) Use your factorizations to solve the system Anx = b, where b=(l,l,l,...,l)T.
(c) Do the entries in the factors approach a limit as n gets larger and larger?