IB Maths AI HL 4.19 – Transition Matrices Notes

IB Maths AI HL 4.19 Notes – Transition Matrices

This IB Maths AI HL 4.19 resource covers Transition Matrices, Markov Chains, and Steady States and is fully aligned with the IB Applications and Interpretation HL syllabus

Students learn how to read and construct transition matrices, understand column-stochastic matrices, and model systems that move between states over time. The concept of a Markov chain is developed, including how to use state vectors and matrix powers to find future distributions.

The resource also introduces steady state (long-term behavior), showing how to solve ( S = TS ) using systems of equations and normalization conditions.

Structured practice questions help students apply transition matrices to real contexts such as market share and radio station listeners.

Ideal for IB Maths AI HL teachers teaching Markov chains and long-term equilibrium modelling.