You should be careful when you multiply matrices - the arrangement of the 2 matrices is important. Take special note of the "green box" on Pg 499, as well as the difference between AB and BA. Then, refer to your textbook Pg 485 onwards where it gives more detailed information on the beginning of the topic.

Complete Exercise A1, A2 and A3 as you finish each section. You should check your answers before moving on to the next section.

(II) Application of Matrices

One of the application of matrices is to solve simultaneous linear equations (SLE). The usefulness of it is that using this method, it is possible to solve SLE of many equations with many unknowns without having very long and tedious working.

You will learn how to use this method to solve SLE where there are 2 equations and 2 unknowns. This is similar to the Sec 2 SLE that you have been dealing with, except that instead of using methods like elimination, substitution and graphical, you use Matrix method instead.

Note that in the exam, you are REQUIRED to use Matrix Method to solve the SLE if the question asks. It is unlike Sec 2, where you can solve SLE via elimination/substitution - in this case, you WILL be specifically asked to USE MATRIX METHOD to solve.

To see how this method is used, refer to your textbook Chapter 1 Section 1.3 from Pg 5 onwards.

Note the terminology "Determinant, Inverse and Singular".

You are only required to know the inverse for 2x2 matrices. Determinants and Inverses of 3x3 matrices and above is not required.

If you prefer to watch videos, here some:

Video 1: Determinant and Inverse of 2x2 matrix (voice is rather soft but the explanation is quite clear)

In addition to the youtube videos below, there are 2 more videos on Matrices.You can view these as well:Matrices Part 1Matrices Part 2Self-study Module (I) - Matrices

## Table of Contents

Duration of self-study: 3 weeks

Mode of Assessment: Test (Earn ACE credits)

What you need to learn:

Resources:

Introduction to Matrices (TB Pg 485 - 503, appendix),

TB Pg 5 - 14 (Section on solving simultaneous equations using Matrix method)

## (I) An introduction to Matrices

To get started, download these notes. Use these notes together with the powerpoint and the textbook.

File Not FoundView these slides to get an idea of what Matrices are and how to perform addition, subtraction and multiplication with matrices.

If you prefer to watch a video, here is one showing

Matrix addition and subtraction: [This video is mute...][URL: http://www.youtube.com/watch?v=YHwNrpUJmog]

Matrix Multiplication Example 1:[URL: http://www.youtube.com/watch?v=qiLjdujcI2w]

Matrix Multiplication Example 2:[URL: http://www.youtube.com/watch?v=Nu0WpF-1_LM]

Matrix Multiplication Example 3:[URL: http://www.youtube.com/watch?v=IRdVU8tyRDU]

Matrix Multiplication Example 4:[URL: http://www.youtube.com/watch?v=N3WT8_TWDYs]

You should be careful when you multiply matrices - the arrangement of the 2 matrices is important. Take special note of the "green box" on Pg 499, as well as the difference between AB and BA. Then, refer to your textbook Pg 485 onwards where it gives more detailed information on the beginning of the topic.

Complete Exercise A1, A2 and A3 as you finish each section. You should check your answers before moving on to the next section.

## (II) Application of Matrices

One of the application of matrices is to solve simultaneous linear equations (SLE). The usefulness of it is that using this method, it is possible to solve SLE of many equations with many unknowns without having very long and tedious working.

You will learn how to use this method to solve SLE where there are 2 equations and 2 unknowns. This is similar to the Sec 2 SLE that you have been dealing with, except that instead of using methods like elimination, substitution and graphical, you use Matrix method instead.

Note that in the exam, you are

REQUIREDto use Matrix Method to solve the SLE if the question asks. It is unlike Sec 2, where you can solve SLE via elimination/substitution - in this case, you WILL be specifically asked toUSE MATRIX METHODto solve.To see how this method is used, refer to your textbook Chapter 1 Section 1.3 from Pg 5 onwards.

Note the terminology "

Determinant,InverseandSingular".You are only required to know the inverse for 2x2 matrices. Determinants and Inverses of 3x3 matrices and above is not required.If you prefer to watch videos, here some:

Video 1: Determinant and Inverse of 2x2 matrix(voice is rather soft but the explanation is quite clear)[URL: http://www.youtube.com/watch?v=iH3CUVI9S4k]

Video 2: This video shows you how to find inverse, as well as how the inverse and the original matrix multiplies to give the identity matrix.[URL: http://www.youtube.com/watch?v=iUQR0enP7RQ]

Video 3: Determinant of 3x3 matrix (optional)[URL: http://www.youtube.com/watch?v=ROFcVgehEYA]

Video 4: Determinant and Inverse of 3x3 Matrix (optional)[URL: http://www.youtube.com/watch?v=NFD8N2sxeCM]

Video 5: Solving SLE using Matrix method[URL: http://www.youtube.com/watch?v=WzIudR-LRg8]

Complete Ex 1.3 and Misc Ex 1 Q10 - Q17. Check your solutions at the back of the book.

## (III) Further exploration [optional, will not be tested]

For further exploration and application of Matrices in real-life, you are encouraged to read up

**http://aix1.uottawa.ca/~jkhoury/cryptography.htm**

to see how Matrices can be applied in

Cryptography.Matrices are also used in

Geometrical Transformations(Enlargement, Rotation, Translation etc). For an example of how it works, download this file:File Not FoundQuizClick on your respective class. Your attempt of the quiz will serve as your attendance for the lesson.3P2:__http://www.thatquiz.org/tq/classtest?FMLC4723__

3N1:__http://www.thatquiz.org/tq/classtest?BUMY2563__