Modelling with matrices
Choose a subtopic, explore its examples and practise with feedback.
Choose a subtopic.
Explore modelling with matrices for Year 12. Each subtopic has sample questions and worked answers; choose the skill you want to practise.
Application of matrices to network problems
Directed network connectivity matrices and orientation; Powers count n-step walks; Weighted sums, connectivity efficiency and dominance models; Limits of matrix path counts/model weightings
Examples, answers and practiceApplication of matrices to transition problems
Row-stochastic transition matrices; Population row vector R and update RT; Repeated predictions and steady state; Effects of transition rates and initial populations; Model assumptions and limitations
Examples, answers and practiceMake, test and investigate.
Build a network and matrix
Create and label a weighted network, verify its matrix and investigate how a changed connection affects a route or flow.
Guided activity · No gradeInvestigate a transition model
Choose transition probabilities and an initial distribution. Iterate the row-vector model, compare stationary proportions with observed convergence and investigate a periodic case.
Guided activity · No grade