VCE Further Mathematics Units 3 and 4 – Matrices

US$4.00 / month with 1 month free trial

✓ Try it Free
✓ 1 Month Free Trial
✓ Instant Learning

✓ Experts Video Lessons
✓ Interactive Practice Tutorials
✓ Exam Style Quizzes
✓ Perfect Online Courses for Home Schooling

Your subscription renews monthly once subscribed.
You can cancel your subscription anytime.

Description

3.1 Matrices
3.2 Transition Matrices
3.3 Matrix Applications




Additional information

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.

You may also like…