Matrix models — Topic Review | Year 12

QUICK RECAP

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 $T^{n} x_{0}$ , with changing rules in the correct time order.

Solve $T s = s$ together with the total, then assess convergence separately.

Check assumptions and compare forecasts with independent observations.

Practice tests

Complete each paper and show your working.

Matrix models — Practice test 1
10 questions · 45 marks · 70 minutes · Technology-assisted
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.
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Matrix models — Practice test 2
10 questions · 45 marks · 70 minutes · Technology-assisted
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.
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Matrix models — Practice test 3
10 questions · 56 marks · 70 minutes · Technology-assisted
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.
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Matrix models — Practice test 4
10 questions · 51 marks · 70 minutes · Technology-assisted
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.
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Matrix models — Practice test 5
10 questions · 52 marks · 70 minutes · Technology-assisted
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.
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Matrix models — Applications test 6
10 questions · 59 marks · 70 minutes · Technology-assisted
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.
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Back to Matrix models

Connect the ideas

Practice tests

Matrix models — Practice test 1

Matrix models — Practice test 2

Matrix models — Practice test 3

Matrix models — Practice test 4

Matrix models — Practice test 5

Matrix models — Applications test 6