• Mathematics General
• Year 12

# Matrices

approx. 15 hrs

2 topics

40 concepts

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

Available in
NT QLD SA TAS VIC WA

### Overview

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.

• #### Applications of Matrices 25 concepts

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

2. Construct a network diagram from a matrix

3. Find the determinant of a 2x2 matrix

4. Find the inverse of a 2x2 matrix

5. Evaluate matrix expressions involving powers

6. Application of permutation matrices

7. Construct a communication matrix from a diagram

8. Construct a dominance matrix

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

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

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

12. Construct a transition matrix from a transition diagram

13. Interpreting a transition matrix

14. Construct a matrix recurrence relation

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

16. Determine the nth state of a system

17. Estimate the steady state solution

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

19. Solve simultaneous equations using application of inverse matrices

20. Determine the transpose of a matrix

21. Use a matrix to represent data tables

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

23. Use matrices to encode a message

24. Use matrices to decode a message

25. Solve simultaneous equations using matrices on a CAS calculator

• #### Operations with Matrices 15 concepts

1. Multiply two matrices using a calculator

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

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

4. Multiply two matrices

5. Determine the order of a matrix product

7. Subtract matrices

8. Perform scalar multiplication of a matrix

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

10. Identify the elements in a matrix using notation

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

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

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

### 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

Reporting

• 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

### Ready to start this program?

Simply pick a time that works for you

We'll book in your first session and match you to an expert tutor

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime