MA1101R Handout123123

MA1101R Linear Algebra I 2013/2014 Semester I

Lecture Hours (@ LT27): Tue 4.00-‐5.30pm/Fri 4.00-‐5.30pm

IVLE WEBPAGE: https://ivle.nus.edu.sg/ Lecturer: Dr Ng Kah Loon Email: [email protected]; Office: S17, #07-‐20; Tel: 6516-‐2751 Assessment: • Final examination 70% -‐ 29th November (9.00 – 11.00am) (2 helpsheets) • Mid-‐term test 20% -‐ Week 7 during either Tue or Fri Lecture (1 helpsheet) • Lab Quiz 10% -‐ Week 13 Aims and objectives: This module serves as an introduction to the most basic concepts in linear algebra that are routinely applied in fields like science, engineering, statistics, economics and operations research. The vector spaces within which the general ideas are developed are all real vector spaces (actually Rn). The objective of the course is to inculcate a facility in both the algebraic and geometric viewpoints of linear algebra. The course will develop basic skills in computing with vectors and matrices. Main topics: Systems of linear equations. Matrices. Determinants. Euclidean n-‐space. Subspaces. Linear independence. Basis and dimension. Rank of a matrix. Orthogonality and orthonormal bases. Eigenvalues and eigenvectors. Diagonalization and orthogonal diagonalization. Linear transformations from Rn to Rm. Applications. Textbook: • The textbook Linear Algebra-‐Concepts and Techniques on Euclidean Spaces (by Ma S.L.,

V. Tan, Ng K.L. published by McGraw Hill) is available for purchase at Co-‐op (Science).

• The lectures will follow the textbook closely. All 7 chapters in the book will be covered. • Students are expected to work through the exercise sets in the books. There is no need

to hand in the answers of the exercises. Selected problems will be discussed during tutorial sessions.

Tutorial sessions: • There are altogether 11 tutorial sessions, starting from week 3. • Each week, selected exercise problems from the textbook for topics that have been

covered in lectures up to the previous week will be discussed. • Students may be asked by their tutor to present solutions.

Lab sessions: • There will be 5 lab worksheets in total. They will be distributed during weeks 4, 6, 8, 11

and 12. • There will be one lab quiz in week 13. • Students will be using MATLAB to complete their worksheets. • There is no formal class structure for lab. Students are allowed to go to the Computer

lab (S17-‐03-‐02) anytime, during the stated times below: o Wednesday 9am – 11am o Thursday 11am – 2pm o Friday 12 – 4pm

• Once a student completes the lab worksheet for that week, he/she will be allowed to leave the lab. No attendance will be taken. There is no need to submit any completed worksheets.

• During the above time slots, there will be a Lab Assistant stationed in the lab to assist students who may have queries.

• If a student is unable to go to the lab in any of the time slots given above (due to timetable clashes), he/she may go to the lab at a time convenient to them, provided the lab is not being used by another module. However, there will not be any Lab Assistant present during other time slots.

• Availability of computers in the lab is on a first come first served basis. The Lab Assistant will resolve any disputes.

• There WILL be formal class registration for the quiz in Week 13. More details will be available in due course.

Signing up for tutorial groups: • NUS students: Through CORS balloting: 16th – 20th August • NUS students: Manual registration (with lecturer, if failure to obtain a group through

CORS balloting): 21st – 22nd August • Exchange and all other non-‐graduating students: Contact lecturer between 13th to 20th

August. • Contact lecturer as soon as possible for any problem with tutorial group.

Online discussion forum • An online forum has been opened for students to post anything (queries, thoughts,

comments, suggestions …) about this module. • Access through module webpage or IVLE. Consultation booking • Lecturer is available for consultation on an ad-‐hoc basis. Prior appointment (via email)

can be made to see the lecturer for consultation/clarification of concepts. • All students are encouraged to seek help early if they have difficulty with the module

and not wait till the last minute. • Reference Books:

Title/ Authors (Remarks) Publisher

Elementary Linear Algebra / Howard Anton (For understanding basic concepts) Wiley

Linear algebra with applications / Steven Leon (With MATLAB exercises) Prentice Hall

Schaum's outline of theory and problems of linear algebra/ Seymour Lipschutz (Plenty of solved problems) McGraw Hill

Linear Algebra/ Stephen H. Friedberg (Advanced reading) Prentice Hall

Week Lecture Tutorial / Lab Remarks

Week 0 5th Aug – 9th Aug

No Lectures

Orientation Week


Lecture 00 (Introduction)

Lecture 01 (Chapter 1)

Week 2 19th Aug – 23rd Aug






Tutorial 01

Week 4 2nd Sep – 6th Sep



Tutorial 02

Lab 01

Week 5 9th Sep – 13th Sep



Tutorial 03

E-‐Learning Week

Week 6 16th Sep – 20th Sep



Tutorial 04

Lab 02

Recess Week 21st Sep – 29th Sep

Week 7 30th Sep – 4th Oct


Mid Term Test

Tutorial 05

Mid-‐ Term Test this week (date to be

advised) Week 8

7th Oct – 11th Oct Lecture 13 (Chapter 3)


Tutorial 06

Lab 03

Week 9 14th Oct – 18th Oct

No Lecture


Tutorial 07

15th Oct (Tue) is a Public Holiday

Week 10 21st Oct – 25th Oct



Tutorial 08

Week 11 28th Oct – 1st Nov



Tutorial 09

Lab 04

Week 12 4th Nov – 8th Nov

Lecture 20 (Chapter 5,6)


Tutorial 10

Lab 05

Week 13 11th Nov – 15th Nov


Lecture 23 (Revision)

Tutorial 11

Lab Quiz

Reading Period 16th Nov – 22nd Nov

Examination 29th Nov (Friday AM)

Tutorial Problem Sets

T1: Chapter 1 Exercise 1: Questions 4, 12, 15, 24, 27, 30



T4: Chapters 2, 3 Exercise 2: Questions 54, 60. Exercise 3: Questions 5, 9, 11, 15



T7: Chapters 3, 4 Exercise 3: Questions 43, 46, 49 Exercise 4: Questions 2, 3, 5




T11: Chapters 5, 6, 7 Exercise 5: Questions 24, 26, 28 Exercise 6 : Questions 24, 28 Exercise 7 : Questions 2, 3

MA1101R Handout123123

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