MA-351 Homework 2

Due at 9:00am, Wednesday September 17, 2003


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 245 before Wednesday, or handed to Brenda Currin before 9am on Wednesday. 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 (b) only.
  2. Consider a 3-D cube as a digraph by letting the arcs point from right-to-left, top-to-bottom, front-to-back. To this, add an arc from the left-back-top vertex to the right-front-bottom vertex. The number of a vertex is the value as a binary number of (left=0/right=1,0=bottom/top=1,0=front/back=1) with the right-bottom-front vertex having the number 4. Please give
    1. the adjacency matrix M by ordering the vertices by ascending numerical value.
    2. the reachability matrix R
    3. write down M3; justify your answer (e.g., "computed in Maple").
  3. DMM, §2.4, Problems 11 on page 59.