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Question 8

From Math Applications HL Paper 1 (May 2025, TZ2)

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  1. [Maximum mark: 6]

A mapping system stores the connections between 5 towns, labelled A, B, C, D and E, in an adjacency matrix. The adjacency matrix, with rows and columns in alphabetical order, is:

Adjacency matrix for 5 towns A, B, C, D, E.
Adjacency matrix for 5 towns A, B, C, D, E.

(a) Draw and label a graph to represent the adjacency matrix. [2]

(b) Determine the number of walks of length 4 which start and end at the same town. [4]