MA2001

Linear Algebra I

Introduction
MA2001

MA2001 Linear Algebra I is a core module of

many different majors and minors in NUS
because the contents of the module have broad
applications on various disciplines.
In the past, the module was coded MA1101R
(before 2021). If you want to find archives from
the library, you can also search for MA1101R.
Lectures

Group 1 (Lecturer: Ma Siu Lun)

Wednesday 10:00 am - 11:30 am at LT32
Frisday 10:00 am - 11:30 am at LT27

Group 2 (Lecturer: Arghya Sadhukhan)

Tuesday 12:00 noon - 1:30 pm at LT31
Thursday 12:00 noon - 1:30 pm at LT31

The time span for each lecture is 1½ hour.

Lecturers

Group 1
Name: A/Prof Ma Siu Lun
Office: S17-07-19
Tel: 6516-3338
E-mail: matmasl@nus.edu.sg

Group 2
Name: Dr Arghya Sadhukhan
Office: S17-05-06
Tel: 6601-4108
E-mail: arghyas0@nus.edu.sg
LumiNUS

All announcements and supplementary materials

will be posted on Canvas:
https://canvas.nus.edu.sg/.

You are advised to check the course web-page in

Canvas more often.
Textbook and Lecture Notes

We follow the textbook closely:

Linear Algebra: Concepts and
Techniques on Euclidean Spaces
(Second Edition)
by S.L. Ma, K.L. Ng and V. Tan,
McGraw Hill, 2016.
You are strongly advised to get a copy.
Please search from the online store of NUS Co-op:
https://www.nuscoop.sg/Linear-Algebra-Concepts-And-Techniques.

There is an online version of the textbook from the

publisher. You can assess through LINC:
https://linc.nus.edu.sg/record=b4220761.
Reference Books

Other reference books:

1. Linear Algebra with Applications by S.J. Leon,
Prentice Hall.
2. Elementary Linear Algebra by H. Anton, Wiley.
You do not need to buy the reference books. You can
borrow the books from the Science Library if you want to
know more about linear algebra.
Syllabus

1. Systems of linear equations, Gaussian elimination.

2. Matrices, matrix operations, invertible matrices,
determinants.
3. Euclidean n-space, linear spans, subspaces, linear
independence, bases.
4. Vector space associated with matrices.
5. Orthogonality, orthonormal bases, orthogonal
projection.
6. Eigenvalues and eigenvectors, diagonalization.
7. Linear transformations.
(Read the Preface of the textbook for the outline of each
chapter.)
Class Components

Learning Components:
1. Lectures (Weeks 1 to 13)
2. Tutorials (Weeks 3 to 13)
3. Labs (Weeks 4, 6, 8, 10)

Assessment Components:
4. 6 Online Quizzes (Weeks 3 to 13, odd weeks) 14%
5. 3 Homeworks (Weeks 5, 8, 12) 12%
6. 1 Lab Assignment (Week 13) 4%
7. Final Exam 70%
Online Quizzes

You need to complete 6 graded online quizzes through

Canvas from Week 3 to Week 13 (the odd weeks). Each
quiz will be based on lectures of the previous two weeks.
You are encouraged to attempt the quiz as soon as
possible.
For each odd week, the quiz will be opened from Monday
00:00 to Friday 23:59. (The deadline is the submission
deadline. It means you need to finish the quiz and click
submit before Friday 23:59. Marks will be deducted
automatically if the answers are received beyond the
deadline.)
Each quiz can be attempted at most 2 times. The grade
of the highest of the attempts will be taken.
Tutorial Classes

You need to attend a tutorial class every week

starting from Week 3.

Your tutor will discuss a list of tutorial questions

(mainly taken from the textbook) with the class.
Please download the tutorial questions from
Canvas and try to work out the solutions before
attending the tutorial class.
Complete solutions to the tutorial questions will
be uploaded to Canvas the week after.
Homeworks

There are 3 graded homeworks.

Please download the homework questions from

Canvas. After you have completed the
homework, you have to submit your answer script
(as a pdf file) through Canvas before the
deadline.
Late submission will be penalized.
MATLAB

A computer program called MATLAB will be used

for our laboratory sessions.
As an NUS student, you can install MATLAB in
one of your personally owned computers.
You have to create a MathWorks account using
your NUS email address:
https://www.mathworks.com/mwaccount/register.
For instructions to install MATLAB, please
download the file MATLAB installing
instruction.pdf from Canvas.
Computing Laboratory

There are 4 laboratory sessions.

The laboratory sessions will be commenced in Weeks 4,
6, 8 and 10. They are optional and you do not need to
register for classes.
For each laboratory session, download the laboratory
worksheet from Canvas and work out the answers using
MATLAB. You are encourage to do the exercises using
your computer. If you really need some guidance, you
can attend one of the laboratory sessions.
Complete answers to the worksheets will be uploaded to
Canvas the week after.
Lab Assignment

After you have completed the 4 laboratory

sessions, there will be a graded lab assignment
in Week 13.
It is an online assignment through Canvas.
Complete and submit the assignment before the
deadline. (You need to use MATLAB to help you
to answer the questions.)
Late submission will be penalized.
Week Date Tutorial Lab Homework Lecture plan Text-book Quiz

Linear Systems, Gaussian

1 14/8-18/8 1.1-1.4
Elimination
Gaussian Elimination (continue),
2 21/8-25/8 1.4-2.2
Matrices Operations

Matrix Multiplication, Inverses,

3 28/8-1/9 1 2.2-2.4 1
Elementary Matrices.

Elementary Matrices (continue),

4 4/9-8/9 2 1 2.4-2.5
Determinants

Determinants (continue), Euclidean

5 11/9-15/9 3 1 2.5-3.2 2
Spaces, Linear Combinations

Linear Spans, Subspaces, Linear

6 18/9-22/9 4 2 3.2-3.4
Independence

23/9-29/9 Term Break

7 2/10-6/10 5 Bases, Dimension, Transition Matrices 3.5-3.7 3

Vector Spaces Associated with

8 9/10-13/10 6 3 2 4.1-4.3
Matrices

9 16/10-20/10 7 Orthogonality, Best Approximation 5.1-5.3 4

Least Squares Solutions, Orthogonal

10 23/10-27/10 8 4 5.3-6.2
matrices, Diagonalization

Diagonalization (continue), Quadratic

11 30/10-3/11 9 6.2-7.1 5
Forms, Linear Transformations

12 6/11-10/11 10 3 Linear Transformations (continue) 7.1-7.3

lab
13 13/11-17/11 11 Revisions 6
assignment
How to study mathematics in this level?

In our textbook, it usually presents a new topic in the

following order: a discussion of the motivation (if any), the
definitions of the main objects of the topic, some
examples, results and properties (theorems and remarks)
deduced from the definitions, more examples.
From our past experience, a lot of students only study
examples and skip definitions, theorems and remarks.
This is a very bad habit which is developed when they are
in secondary school. But such a way of study does not
work in this level any more.
How to study mathematics in this level?

The reason why you can do it in the secondary school is

that mathematics in the secondary school is basically
about problem solving. So you can learn the methods
from examples.
However, in this level, we are building up mathematical
theories. For example, the aim of our module is to build
up a theory of vector spaces. It is no longer just problem
solving.
To study mathematics in this level, you need to first
understand the definitions thoroughly. Then try to follow
how the results and properties are derived. The
examples are just to help you to understand the concept.
How to study mathematics in this level?

If you have any problems, ask early (either ask the lecturer
or tutor), especially the first three chapters. Since we are
building a theory, anything you don't understand at the
beginning will affect later topics.
In every quiz, tutorial worksheet and homework assignment,
there is always a statement asking you to revise certain
topics before attempting the questions. Take the advice
seriously. Don't try to read the questions first and then
search for similar examples from the textbook. This will not
work because some questions asked are based on the
theory itself and may not have a similar example. You need
to understand the materials from the mentioned topics
before you can do those questions.