# Incidence Matrices

Sears airways is a budget airline. On a particular day, it has flights connecting 4 cities, Singapore, Taipei, Seoul and Tokyo. The flights can be represented by the following network, with arrows indicating the direction of the flights. [map of network)

The incidence matrix shows whether it is possible to travel directly from one city to another.

             End of flight      start of flight
A   B   C   D
0   1   0   0      A


M= 1 0 1 1 B 1 0 0 1 C 0 1 1 0 D a)Using Matrix multiplication calculate M^2. Explain what entries in M^2 represent b)Calculate M^2 + M . This matrix does not contain zero entry. What is the meaning of absence of zero entry?

My answer: M^2= 1 0 1 1 1 2 1 1 0 2 1 0 2 0 1 2

Entry 1 means one return jorney from the start of flight to end of flight is possible. Entry 2 means 2 return journeys are possible. am I right? M^2+M= 1 1 1 1 2 1 2 2 1 2 1 1 2 1 2 2 I don't know how to make sense of this matrix. what does the absence of zero mean? Please help. Thank you . Ashwini

• The matrices are not readable at all, as you can see. Please rewrite the matrices, and you can use MathJax for that. – Matti P. Feb 11 at 9:55
• i had uploaded picture which does not show here – Ashwini Feb 11 at 9:55
• I would advice not to post links to pictures -- posts on this forum should be self-contained. Please type out the matrices with MathJax. – Matti P. Feb 11 at 9:56