Summer Session 2
July 6

Show that trace of AB = trace of BA

Show that (AB  BA)(AB  BA) is scalar

Find all matrices commuting with .

Show that A^{1}BA can never be diagonal.

Show that there is no real invertible matrix S with S^{1}S
triangular.
Spreadsheet in Maple

Use the spreadsheet in Maple to experiment with the 3x + 1 problem.

How is the number pattern related to the sucessive derivatives of tan(x)
formed?

How is the number pattern related to the sucessive derivatives of cot(x)
formed?

Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.

Study the number pattern associated with the indefinite integral of the
function x^{n}e^{x}.

List the Chebyshev polynomials T_{n}(x) for n = 0,1,2,3,4,5,6.
Factoring