Let , be scalars. Let T, be the n n tridiagonal matrix that has all

Question:

Let α, β be scalars. Let Tα,β be the n × n tridiagonal matrix that has all or's on the sub- and superdiagonals, and β's on the main diagonal.
(a) Solve the iterative system u(k+l) = Tα,βu(k).
(b) For which values of α, β is the system asymptotically stable? Combine Exercises 10.2.13 and 10.1.30.