VCE Further Mathematics Units 3 and 4 – Matrices

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3.1 Matrices
3.2 Transition Matrices
3.3 Matrix Applications

Additional information


Key knowledge
• the order of a matrix, types of matrices (row, column, square, diagonal, symmetric, triangular, zero, binary, permutation and identity), the transpose of a matrix, elementary matrix operations (sum, difference, multiplication of a scalar, product and power)
• the inverse of a matrix and the condition for a matrix to have an inverse, including determinant
• communication and dominance matrices and their application
• the use of matrices to represent and solve a system of linear equations
• transition diagrams and transition matrices and regular transition matrices and their identification.

Key skills
• use the matrix recurrence relation: \( S_0 = \) initial state matrix, \( S_{n+1} = TS_n \) to generate a sequence of state matrices,
including an informal identification of the equilibrium or steady state matrix in the case of regular state matrices
• construct a transition matrix from a transition diagram or a written description and vice versa
• construct a transition matrix to model the transitions in a population with an equilibrium state
• use the matrix recurrence relation \( S_0 = \) initial state matrix, \( S_{n+1} = TS_n + B \) to extend the modelling to populations
that includes culling and restocking.

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