• Mathematics General
  • Year 12


approx. 15 hrs

2 topics

40 concepts

Deepen your understanding of Matrices and the skills to approach your examinations with confidence.

Available in


Year 12 Matrices is a learning program that covers the essential components of Year 12 General Mathematics and is aligned with the Australian curriculum.  As part of this course, students develop their ability to conduct mathematical operations with matrices, and to apply matrices to solve practical problems, including the use of permutation, communication and dominance matrices.

Topics & Concepts We Cover

This learning program is made up of the following 2 topics, broken down into 40 concepts.

  • Operations with Matrices 15 concepts

    1. Use of a rule for the aijth element of a matrix to construct the matrix

    2. Use summing matrices to sum the rows and columns of matrices

    3. Multiply two matrices using a calculator

    4. Perform scalar multiplication of a matrix

    5. Subtract matrices

    6. Multiply two matrices

    7. Determine the order of a matrix product

    8. Add matrices

    9. Calculate the sum of elements in a row or column

    10. Identify the elements in a matrix using notation

    11. Identify different types of matrices including row, column, square, identity, diagonal, triangular, symmetric and zero

    12. Use the matrix template of the calculator to retrieve values of elements

    13. Perform a combination of addition, subtraction and scalar multiplication of matrices

    14. Use a calculator to perform operations with matrices

    15. Write down the order of a matrix

  • Applications of Matrices 25 concepts

    1. Determine the nth state of a system

    2. Application of permutation matrices

    3. Construct a matrix recurrence relation

    4. Find the determinant of a 2x2 matrix

    5. Evaluate matrix expressions involving powers

    6. Find the inverse of a 2x2 matrix

    7. Find the determinant and the inverse of an nxn matrix using a calculator

    8. Construct a communication matrix from a diagram

    9. Construct a dominance matrix

    10. Construct a network diagram from a matrix

    11. Construct a transition matrix from a transition diagram

    12. Interpreting a transition matrix

    13. Application of binary matrices to model and solve a range of word problems

    14. Construct a matrix to represent connections of a network diagram

    15. Estimate the steady state solution

    16. Using the determinant test to identify simultaneous equations with no solution

    17. Use a recursion relation to calculate state matrices step-by-step

    18. Determine the transpose of a matrix

    19. Solve simultaneous equations using application of inverse matrices

    20. Application of matrices to solve a range of word problems

    21. Use matrices to encode a message

    22. Use a matrix to represent data tables

    23. Solve simultaneous equations using matrices on a CAS calculator

    24. Use matrices to decode a message

    25. Use of powers of matrices to model and solve word problems

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Matrices


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

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Starting at

$49(inc. GST)

per session

Fully flexible

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Access to practice questions

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