Welcome Note

Matrix and Algebra Expressions is a 5-day pure online course. It is a comprehensive, flexible and fully supported environment for personalized online learning. This course will help the participants to master matrices and algebra expressions as proper guidance is available throughout the course.  With minimum pre-requisite, candidates will be able to learn and explore more on this interesting topic.

The main purpose of this course which is conducted fully online is to provide the flexibility needed to create highly personalized learning. Participants can complete all the coursework and do self-learning from anywhere and anytime as long as they have an internet connection. It is highly advisable that all participants adhere to putting in the needed effort on a daily basis and this includes doing activities, participating in discussions, attempting assignments and doing a lot of self-readings. The course will use the following  web tools : facebook, wikispace, proboards, GoogleDoc, YouTube, scribd and SlideShare. We believe that the use of these web tools will indirectly help to maximize the achievement of participants. All participants are required to review the schedule, and please pay careful attention to deadlines as the deadlines will not be extended at all for a short 5-Day course.

Upon completion of this course, all participants will receive two certificates which indicate the participation evidence and grade obtained respectively. The grade will be categorized based on the results obtained from the 4 sets of tests and a project. Participant work output will be graded as:  Excellent, Good, Satisfactory or Unsatisfactory.

All materials and relevant resources are available online. You may access the materials by clicking at the links on the right-hand side of the screen or scroll down directly from the course link (OCTOBER) to continue your course.

If you have any further inquiries about the course, please send an email to our facilitators at the following emails : noorehas@yahoo.com, an_nie_koh@yahoo.com, or yus12linda@yahoo.com or alternatively you may communicate with us  through facebook.

 
Samuel Johnson: Student Motivation Quotes
Great works are performed not by strength but by perseverance.

Course Description

This course is made up of 2 major topics, i.e. Matrix and Algebra. The details are as follows:

Topic: Matrix

Prerequisite: Basic Mathematics knowledge.

This topic includes matrices up to 3x3 order.

Topic: Algebra Expressions

Prerequisite: Pre-Algebra with a minimum of a pass in mathematics.

This course includes a review of basic topics from intermediate algebra to higher level algebra.  

 

R. D. Clyde

Getting things done is not always what is most important. There is value in allowing others to learn, even if the task is not accomplished as quickly, efficiently or effectively

 

Contents of this blog

Thomas Alva Edison
Genius is one per cent inspiration and ninety-nine percent perspiration.



 

a) Course Outline

a) Facilitators’ names

b) Daily study schedule (Refer to the course topics)

c) Course resources (notes, videos and slides)

d) Study Approach

e) Assessment details

Facilitators

Lead Facilitator: Ms Nooreha Ahmad

Assistant Facilitators:

1. Ms Yuslinda Yusof

2. Mr Tan Seow Pin

3. Ms Fauziah Ahmad

4. Ms Koh An Nie

What Should You Do First ?

1. View the learning outcomes.

2. Review the daily course topics and do daily readings and assessment

3. Perform the student readiness checklist .

    to ensure that you understand clearly, what to do before starting the course.

 

" True greatness is not achieved with a quarter-mile lead and no rival in sight; it is grasped in the last hundred feet when one displays pure valiancy and conquers those more capable than himself."
Written in 2010 by Maxwell Schwam --- Tennessee

Course Learning Outcome

Upon completion of this course, learner will be able to:

1. Recognise different types of matrices, given a variety of matrices
2. Identify the order of matrix and the elements in the correspondence position.
3. Evaluate determinants up to 3x3
4. Apply basic operation on matrix
5. Solve three simultaneous linear equations.
6. Use matrix to solve a set of linear equations using inverse matrices.
7. Use the concept of Algebra expression to solve equations or polynomials.
8. Simplify algebraic expressions by collecting like terms and by abstracting common factors from similar terms. 
9. Use different methods to solve algebra expressions .

Study Approach

To ensure you will successfully complete the course within the five

days, please do the following:

1. Do the assessment ( self assessment as well as daily assessment )

    that has been finely planned for you daily.

2. Contribute your ideas as well as discussions in the comment box

    and share it with the facilitator  and other participants.

3. You have to read a lot on your own. 

 " Fix your goal, plan the activity and start executing each step with a constant intensity, 

vigor & pure thoughts till you reach the goal."
Written in 2010 by Karabi Paattnaik --- India

Course Outline

Day 1-2 - Matrix

1. Introduction of Matrix
2. Size of Matrix
3. Determinants
4. The transpose of a matrix
5. Addition, subtraction and multiplication
6. Cramer’s Rule
7. Row Operation
8. Inverse Matrix

Day 3-5 – Algebra

1.      Introduction of Algebra

2.      +, -, x, ÷ on simple polynomials.

3.      Factorising: Simplifying algebraic fractions.

       - factorising

      - difference of square

       - theorem

4. Transfer of model data to analysis programs.    

5. Solving one variable equations

  - to evaluate the value of the alphabetic terms

6. Partial fractions

nly when you are willing to work for something, harder than anyone else on this earth, does it deserve to be yours.

Day 1

The term "matrix" for such arrangements was introduced in 1850 by  

James Joseph Sylvester.

Sylvester, incidentally, had a (very) brief career at the University of Virginia,
which came to an abrupt end after an enraged Sylvester hit a newspaper-reading
student with a sword stick and fled the country, believing he had killed the student!

( Interesting isn't it ? Want to know more ? Read the history of James
  Joseph Sylvester,the great mathematician who has created matrices )

Assessment Details

Ongoing Assessment : 100 marks.

Day 1 : Test 1 - 20 marks

Day 2 : Test 2 - 20 marks

Day 3 : Test 3 - 20 marks

Day 4 : Test 4 - 20 marks

Day 5 : Project - 20 marks

Matrices

Any data that is written in columns and rows can be represented as a matrix. Matrices are used to represent real-world data  such as the foods, drinks or others

Examples :

Types of Foods

Gender	Hotdog	Burger	Sandwich	Sushi
Boy	8	9	4	3
Girl	5	13	0	1

Table above Expressed as Matrix 

 

1. Introduction of Matrix

       1. Read the following  resources:

        -       Module notes :  Different types of matrices.   

   If you still do not understand you can read Types of Matrices.

2.  View the question posted by the lecture and discuss the question in the 
     proboards forum.

     Discussion - Types of Matrices

3. Attempt the True/False Questions. Then refer to the answers provided
   and check how many questions that you attempted is correct. 
    Short explanation is given for each answer. Good Luck...

Types of Matrices

2. Size of Matrix

1. Do you know how to read a matrix ?  

2. Do you know how to identify the position of the elements in the matrix? 

3. Do you know how to identify the elements in the particular position in the matrix? 

All the above questions will be answered after you view the videos below.


1. View other link to enhance your understanding on the

    particular topic

    a)  Reading the size of the matrix.  ( Video 1/14 )

    b) Size of matrix

2. Do the tutorial to enhance your knowledge on size of matrix.

ave courage to do things differently, because 
following the same path will never give 
different results.

3. Determinants

1. View the video in the link below.
    Video 1
    View only the determinant topic. Video part 4/14 under matrices.
    The methods shown in the video above is slightly different from the video
    below.
 
    Video 2
    This is another method of finding determinants. View this video now.

2. After viewing the two videos above which methods do u think is easy to
    apply in order to evaluate determinants up to 3 x 3 matrices ?
    Discuss this in the forum discussions.
   
3. Here is a quiz for you to try out. Full solutions will be shown if you
    have chosen the correct answer. Good Luck...

f you have built castles in the air, your work need not be lost;

that is where they should be.
Now put foundations under them.

Henry David Thoreau

 

4. Transpose of a matrix

1. Read about transpose.

2. From the website above, what do you understand about transpose of a
    matrix ?
    Discuss about it in Forum Discussions.

3. Please take note that Transpose of a matrix is always denoted by a symbol
    'T'.

 hey can because they think they can.
Virgil

5. Addition, subtraction and multiplication

Success is the sum of small efforts, repeated day in and day out.
Robert Collier

1. View the videos and you will be exposed to the four basic operations
of matrices.The four basic operations are addition, subtraction,
multiplication and scalar product.
a) Operations on matrices
( Video 2/14 and Video 3/14)
b) Video on Addition and Subtraction of Matrices.

2. Then try out this exercise .

“You are the embodiment of the information you choose to accept and act upon. To change your circumstances you need to change your thinking and subsequent actions.”

Test 1

Day 1 ( Test )

Do the test below and submit to the facilitator by email. The email address is indicated clearly in the question paper. Total marks in Test 1 is 50 marks. The marks will then be converted to 20%.

Please show all the solutions in detail. ( Test 1 )

“Don't wait until everything is just right. It will never be perfect. There will always be challenges, obstacles and less than perfect conditions. So what. Get started now. With each step you take, you will grow stronger and stronger, more and more skilled, more and more self-confident and more and more successful.”

Day 2

Summary of Day 1

Nothing can stop the man with the right mental attitude from achieving his goal; nothing on earth can help the man with the wrong mental attitude.
Thomas Jefferson

Basic Definitions 

 

An m×n matrix A is a rectangular array of real numbers with m rows 

and n columns. (Rows are horizontal and columns are vertical.) The

numbers m and n are the dimensions of A.The real numbers in the 

matrix are called its entries. The entry in row i and column j is 

called a_ij or A_ij.

Example

Following is a 4×5 matrix with the entry A₂₃ highlighted. 

A =		0	1	2	0	3
		1/3	-1	10	1/3	2
		3	1	0	1	-3
		2	1	0	0	1

Operations with Matrices

Transpose

The transpose, A^T, of a matrix A is the matrix obtained from A

by writing its rows as columns. If A is an m×n matrix and B = A^T, 

then B is the n×m matrix with b_ij = a_ji. 

Examples  

Transpose

0 1 2 T 1/3 -1 10

=

0 1/3 1 -1 2 10

Sum, Difference If A and B have the same dimensions, then their sum, A+B, is obtained by adding corresponding entries. In symbols, (A+B)ij = Aij + Bij. If A and B have the same dimensions, then their difference, A - B, is obtained by subtracting corresponding entries. In symbols, (A-B)ij = Aij - Bij. Scalar Multiple If A is a matrix and c is a number (sometimes called a scalar in this context), then the scalar multiple, cA, is obtained by multiplying every entry in A by c. In symbols, (cA)ij = c(Aij). Sum & Scalar Multiple 0 1 1/3 -1 + 2 1 -1 2/3 -2 = 2 -1 5/3 -5 Product If A has dimensions m×n and B has dimensions n×p, then the product AB is defined, and has dimensions m×p. The entry (AB)ij is obtained by multiplying row i of A by column j of B, which is done by multiplying corresponding entries together and then adding the results.  Product 0 1 1/3 -1 1 -1 2/3 -2 = 2/3 -2 -1/3 5/3

6. Cramer’s Rule

1. View the video below under the topic Cramer's Rule
for matrices up to 3x3 (video part 12/14).

2. Then read Cramer's Rule for matrices up to 2x2.

3.Try out this quiz. How is it get going ? Need more quiz ? Well, then you
can try some of the quizzes listed below.
1. Cramer's Rule 1
2. Cramer's Rule 2
3. Cramer's Rule 3

3. If you are satisfied with your lesson. Do the self assessment
for matrix 2 x 2 now. Then do the self assessment for matrix 3 x3 .
Type your answer in Ms Words and send it back to the
facilitator (Ms Koh).

Tough times never last, but tough people do.
Dr. Robert Schuller



“Shoot for the moon. Even if you miss, you'll land among the stars.”