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Question
CBSEENMA12034305
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. Below is given the network of bus routes connecting the different bus stands of two cities X and Y : 



(a) Find the network may ices connecting the cities :

(i) X to Y    (ii) Y to X

(b)What is the relation between the far network matrices obtained in (a) above ?

 



Solution

(a) (i) We describe the number of bus routes from X to Y as below :


This is written in the matrix form as
open square brackets table row 1 cell space 1 end cell cell space 0 end cell row 0 cell space 0 end cell cell space 1 end cell row 0 cell space 0 end cell cell space 1 end cell end table close square brackets

(ii) We describe the number of bus routes from Y to X as below

This is written in the matrix form as
open square brackets table row 1 cell space 1 end cell cell space 0 end cell row 1 cell space 1 end cell cell space 0 end cell row 0 cell space 0 end cell cell space 1 end cell end table close square brackets
(b) Matrix for the far net work
equals space open square brackets table row 1 cell space space 1 end cell cell space space 0 end cell row 0 cell space space 1 end cell cell space space 1 end cell row 0 cell space space 0 end cell cell space space 1 end cell end table close square brackets space space open square brackets table row 1 cell space space 0 end cell cell space space 0 end cell row 1 cell space space 1 end cell cell space space 0 end cell row 0 cell space space 1 end cell cell space space 1 end cell end table close square brackets space equals space open square brackets table row cell 1 plus 1 plus 0 space end cell cell space 0 plus 1 plus 0 end cell cell space space 0 plus 0 plus 0 end cell row cell 0 plus 1 plus 0 end cell cell space 0 plus 1 plus 1 end cell cell space space 0 plus 0 plus 1 end cell row cell 0 plus 0 plus 0 end cell cell space 0 plus 0 plus 1 end cell cell space space 0 plus 0 plus 1 end cell end table close square brackets equals space space open square brackets table row 2 cell space space 1 end cell cell space space 0 end cell row 1 cell space space 2 end cell cell space space 1 end cell row 0 cell space space 1 end cell cell space space 1 end cell end table close square brackets

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