Matrices and networks.
Organise quantities with matrices, then model routes, connections, installation cost and capacity-limited flow using stated objectives and constraints.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Matrix organisation and order
Read a rectangular array and explain what its entries mean.
- 02
Matrix arithmetic
Combine matching entries and interpret a scalar multiplier.
- 03
Matrix multiplication
Calculate row-by-column products and check their dimensions.
- 04
Costing/inventory models
Model stock changes and order costs using labelled matrices.
- 05
Reading directed/weighted networks
Read direction, weights and permitted journeys in a network.
- 06
Network terminology and connectivity
Describe degrees, connected components, bridges and cycles.
- 07
Counting paths with restrictions
Count routes systematically and interpret powers of an adjacency matrix.
- 08
Shortest/longest paths
Find shortest paths and handle longest routes only under finite stated restrictions.
- 09
Minimum spanning trees including Prim's algorithm
Connect every vertex at minimum total installation cost using a spanning tree.
- 10
Maximum-flow models
Conserve flow, respect capacities and certify a maximum with a matching cut.
- 11
Interpreting the practicality of a solution
Turn a matrix or network calculation into a recommendation that acknowledges constraints and assumptions.
Topic review
Revisit the key ideas, then choose a practice paper.