Let b =
0 2 1
1 1 2
2 1 1
represent the bus routes between 3 cities.
a. draw an example of a network diagram represented by this matrix.
b. calculate the matrix b2 = b.
c. how many routes are there between city 1 and city 2 with one stop in between?
d. how many routes are there between city 2 and city 2 with one stop in between?
e. how many routes are there between city 3 and city 2 with one stop in between?
f. what is the relationship between your answers to parts (b)–(e)? formulate a conjecture