# VCE Further Mathematics Units 3 and 4 – Matrices

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## Description

3.1 Matrices
3.2 Transition Matrices
3.3 Matrix Applications

Outcome 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.