Topic 2: Modelling with Matrices

3 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How can matrices store the connections in a network and count routes between vertices?

Represent networks with adjacency matrices and use matrix powers to count walks of a given length between vertices.

How to build an adjacency matrix from a network, read direct connections, and use powers of the matrix to count the number of two-step and longer walks between vertices.

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How do we predict the future state of a system that moves between categories at fixed rates?

Use transition matrices and an initial state vector to predict future states and to find the long-term steady state of a system.

How to set up a transition matrix from movement percentages, apply it to an initial state to predict future states, and find the long-term steady state of a system.

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How do we add, scale and multiply matrices, and when is each operation defined?

Perform matrix addition, subtraction, scalar multiplication and matrix multiplication, applying the order and conformability rules correctly.

How to read a matrix order, add and subtract matrices, multiply by a scalar, and multiply two matrices using the row-by-column rule, including when each operation is defined.

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