MA-351 Homework 2

Due at 9:00am, Monday September 16, 2002

Calculations necessary for these problems may be done either by hand or with Maple. Handwritten solutions may be submitted to me or put in my mailbox in HA 243 before Monday, or handed to Brenda Currin before 9am on Monday. Or you may email before the deadline an ASCII text, Maple Worksheet (.mws), html, or postscipt/pdf-formatted document to me (kaltofen@math.ncsu.edu).
Note my office hours on my schedule.

1. DMM, §2.3, Problem 1 on page 49 for graph (a) only.
2. Consider a 3-D cube as a digraph by letting the arcs point from left-to-right, bottom-to-top, back-to-front. To this, add an arc from the right-back-top vertex to the left-front-bottom vertex. The number of a vertex is the value as a binary number of (left=0/right=1,bot/top,front/back) with the right-bot-front vertex having the number 4. Please give
   1. the adjacency matrix M
   2. the reachability matrix R
   3. write down M³; justify your answer (e.g., "computed in Maple").
3. DMM, §2.4, Problems 9 and 10 on page 59. Note that RxR' means R *_element-wise R' according to the book. R' means the transposed of R, i.e., where the elements are swapped along the diagonal.