• 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.

• #### 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. Multiply two matrices using a calculator

6. Determine the order of a matrix product

7. Multiply two matrices

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

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

10. Perform scalar multiplication of a matrix

11. Add matrices

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

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

3. Construct a matrix recurrence relation

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

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

6. Construct a communication matrix from a diagram

7. Construct a network diagram from a matrix

8. Construct a transition matrix from a transition diagram

9. Estimate the steady state solution

10. Determine the nth state of a system

11. Evaluate matrix expressions involving powers

12. Interpreting a transition matrix

13. Construct a dominance matrix

14. Application of permutation matrices

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

16. Find the inverse of a 2x2 matrix

17. Find the determinant of a 2x2 matrix

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

19. Use a matrix to represent data tables

20. Use matrices to encode a message

21. Use matrices to decode 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 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 Add your payment details securely online We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

Enquire now