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

    4. Identify the elements in a matrix using notation

    5. Determine the order of a matrix product

    6. Multiply two matrices using a calculator

    7. Multiply two matrices

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

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

    10. Subtract matrices

    11. Perform scalar multiplication of a matrix

    12. Add matrices

    13. Write down the order of a matrix

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

    15. Use a calculator to perform operations with matrices

  • Applications of Matrices 25 concepts

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

    2. Find the inverse of a 2x2 matrix

    3. Construct a network diagram from a matrix

    4. Find the determinant of a 2x2 matrix

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

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

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

    8. Determine the nth state of a system

    9. Construct a matrix recurrence relation

    10. Estimate the steady state solution

    11. Evaluate matrix expressions involving powers

    12. Construct a communication matrix from a diagram

    13. Construct a dominance matrix

    14. Application of permutation matrices

    15. Interpreting a transition matrix

    16. Construct a transition matrix from a transition diagram

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

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

    19. Use a matrix to represent data tables

    20. Use matrices to decode a message

    21. Use matrices to encode a message

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

    23. Determine the transpose of a matrix

    24. Solve simultaneous equations using application of inverse matrices

    25. Solve simultaneous equations using matrices on a CAS calculator

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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