MAPLE 6  -  2000 Summer Session 2

---

About Two-By-Two Matrices

• 2-1 Show that trace of AB = trace of BA
• 2-2 Show that (AB - BA)(AB - BA) is scalar

• 2-3 Find all matrices commuting with .
• 2-4 Show that A-1BA can never be diagonal.
• 2-5 Show that there is no real invertible matrix S with S-1S triangular
 
Spreadsheet in Maple
• 2- 6 Use the spreadsheet in Maple to experiment with the 3x + 1 problem.
• 2- 7 How is the number pattern related to the sucessive derivatives of tan(x)

      formed?
• 2- 8 How is the number pattern related to the sucessive derivatives of cot(x)

      formed?
• 2- 9 Express tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6.
• 2-10 Study the number pattern associated with the indefinite integral of

        the function xnex.
• 2-11 List the Chebyshev polynomials Tn(x) for n = 0,1,2,3,4,5,6.