IB Math AI AHL 3.15 - Adjacency Matrices

This IB Math AI HL 3.15 – Adjacency Matrices slide deck develops a powerful matrix-based approach to analyzing graphs and networks. The lesson introduces adjacency matrices as a structured way to represent connections between vertices and shows how matrix powers can be used to count walks of a given length between nodes.

Students learn to interpret entries of ( A^k ) in context, linking algebraic results to real-world networks such as road systems. The lesson extends this reasoning to directed and weighted graphs, helping learners interpret weights as costs, distances, or travel times. Transition matrices are also introduced, connecting graph theory to probabilistic modeling and state transitions.

With its strong emphasis on interpretation, structured methods, and exam-style practice problems, this slide deck supports HL-level classroom instruction and independent study, equipping students with the tools needed to confidently analyze networks using matrices in IB Mathematics assessments.