Connect the ideas.
- Label rows and columns before interpreting matrix entries.
- Check dimensions and meaning before matrix multiplication.
- Adjacency powers count exact-length walks and permit repeats.
- Reachability, dominance and shortest distance are different questions.
- Use column state vectors and columns=current for transition matrices here.
- Closed transition matrices have nonnegative probability entries and columns summing to 1.
- Repeated predictions use , with changing rules in the correct time order.
- Solve together with the total, then assess convergence separately.
- Check assumptions and compare forecasts with independent observations.
Put it together.
Choose a paper and show your working.
Matrix models — Practice test 1
Core techniques, network interpretation and two-state forecasts. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 45 marks · 70 minutes · Technology-assistedMatrix models — Practice test 2
Route networks, changing rules and evidence for a model. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 45 marks · 70 minutes · Technology-assistedMatrix models — Practice test 3
Transition estimation, three-state balance and forecast comparison. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 56 marks · 70 minutes · Technology-assistedMatrix models — Practice test 4
Structure, exceptional behaviour and careful interpretation. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 51 marks · 70 minutes · Technology-assistedMatrix models — Practice test 5
Sales, service networks and operational decisions. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 52 marks · 70 minutes · Technology-assistedMatrix models — Applications test 6
Linked models, inference and justified recommendations. Network matrices use rows=start and columns=destination; transition matrices use columns=current and rows=next unless stated otherwise.
10 questions · 59 marks · 70 minutes · Technology-assisted
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 2 General Mathematics matrix-models option. This is the offered fifth-topic option, alongside the four compulsory topics; a school-designed Open Topic is an alternative, not prescribed content in this chapter.
Official curriculum source ↗