Let a =
1 3 2
3 1 2
4 3 2
and b =
2 1 3
2 2 1
1 3 1
represent the bus routes of two companies between three cities.
a. let c = a ⋅ b. find matrix c, and explain the meaning of entry c1,3.
b. nina wants to travel from city 3 to city 1 and back home to city 3 by taking a direct bus from company a on
the way to city 1 and a bus from company b on the way back home to city 3. how many different ways are
there for her to make this trip?
c. oliver wants to travel from city 2 to city 3 by taking first a bus from company a and then taking a bus from
company b. how many different ways can he do this?
d. how many routes can oliver choose from if he travels from city 2 to city 3 by first taking a bus from
company b and then taking a bus from company a?