| 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-1
S triangular. |
| 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. |
| 2-12 |
Find an exponent n such that some coefficients
appearing in the
factorization of xn - 1 are different from 0, -1 and 1. |
| 2-13 |
Factor (((x2 - a)2 - a)2 - a)2 - a - x. |