 2-1Show
that trace of AB = trace of BA |
| 2-2Show
that (AB-BA)(AB-BA) is scalar |
2-3Find
all matrices commuting with  |
| 2-4Show
that A^(-1)BA can never be diagonal. |
2-5Show
that there is no real invertible matrix S with S-1S  triangular |
| 2-6Use
the spreadsheet in Maple to experiment with the 3x + 1 problem |
| 2-7How
is the number pattern related to the sucessive derivatives of tan(x) formed? |
| 2-8How
is the number pattern related to the sucessive derivatives of cot(x) formed? |
| 2-9Express
tan(nx) as a rational function of tan(x) for n = 1,2,3,4,5,6. |
| 2-10Study
the number pattern associated with the indefinite integral of the function
x^n*e^x |
| 2-11List
the Chebyshev polynomials Tn(x) for n = 0,1,2,3,4,5,6. |
| 2-12Find
an exponent n such that some coefficients appearing in the factorization
of x^n - 1 are different from 0, -1 and 1. |
| 2-13Factor
(((x^2 - a)^2 - a)^2 - a)^2 - a - x. |