MTH4115 / MTH4215 - Vectors and Matrices - 2023/24
Topic outline
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This forum is available for everyone to post messages to. If you have any questions about the module, please ask them here.
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These are the typed lecture notes of this module. The file might be updated during the term to correct typos and add problems.
Hand written notes are available under each teaching week below. Note that Dr. Matthew Lewis teaches directly on the board. To obtain Hand-written lecture notes from lectures taught by Dr Lewis, you should watch the QReview videos both for the single and joint honor lectures.
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There will be five summative (assessed) courseworks (to be submitted online, and will be marked automatically).
Each coursework will count 4% and will take place in week 3, 5, 8, 10, 12. The topics will be announced closer to the time.
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Format of the final exam
There will be an on-campus, closed-book final exam worth 80%.
A sample exam with solutions will be provided before the exam period see the tab "Sample exam 2023/2024 and past exam papers". The exam will be based on the problems solved in class.
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1. Vectors in R2 and R3: Coordinates and position vectors; bound vectors, free vectors; vector operations (addition, scalar multiplication, scalar and vector product – definition in terms of coordinates and then geometric interpretation); lengths of vectors.
2. Lines and planes: vector and Cartesian equations; distances between points, lines and planes; intersection of lines and planes, systems of linear equations with 2 or 3 unknowns, solution by Gaussian elimination.
3. Systems of linear equations with n unknowns: Matrix representation as vector equation in Rn; Solution by Gaussian elimination using row operations on matrix of coefficients; echelon forms; existence and uniqueness of solutions.
4. Matrix Algebra: Addition and multiplication. Matrix inverse. Matrix transpose. Special types of square matrices. Conditions for non-singularity.
5. Determinants: Cofactors and row/column expansions. Evaluation using elementary row/column operations. Determinant of matrix transpose and of product of matrices (without formal proofs).
6. Linear transformations of Rn. Basic properties; matrix representation (with respect to the standard basis). Rotations in R2 and reflections in R3
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Academic Content
This module covers:
- Vectors and vector operations in ℝ3.
- Lines and planes in ℝ3.
- Systems of linear equations in n variables and Gaussian elimination.
- Linear transformations in ℝn and the corresponding matrices in ℝ2 and ℝ3.
Disciplinary Skills
At the end of this module, students should be able to:
- Form sums of vectors in ℝ2 or ℝ3 ; form vector product of two vectors in ℝ3.
- Use scalar product to calculate the length of a vector and the cosine of the angle between two vectors in ℝ2 or ℝ3.
- Convert between vector and Cartesian equations of a straight line in ℝ2 or ℝ3 and write equation of a line in ℝ2 or ℝ3 passing through given points, or passing through a point and orthogonal to a line/plane.
- Find all solutions of a set of linear equations in several variables by reduction to echelon form.
- Add and multiply two matrices and calculate the inverse of an invertible matrix.
- Calculate the determinant of a square matrix, and determine its invertibility using the determinant.
Calculate the matrix corresponding to a given linear transformation of ℝn.
Attributes
At the end of this module, students should have developed with respect to the following attributes:
- Grasp the principles and practices of their field of study.
- Acquire substantial bodies of new knowledge.
- Explain and argue clearly and concisely.
- Acquire and apply knowledge in a rigorous way.
- Connect information and ideas within their field of study.
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In this folder you will find the teaching material of week 1. We covered from Chapter 1, 2 till 3.1.4 in the typed pdf lecture note. For hand-written notes for single honor thursday or both lectures of joint honor (Mon. and Fri.) taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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In this folder you will find the teaching material for week 2. For hand-written notes for single honor thursday taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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In this folder you will find the teaching material for week 3. For hand-written notes for single honor thursday or both lectures of joint honor (Mon. and Fri.) taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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In this folder you will find the teaching material for week 4. For hand-written notes for single honor thursday taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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In this folder you will find the material for week 5 and also the link to access the quiz opening at 2pm on Thursday 22/02 and closing at 2pm on Friday 23/02.For hand-written notes for single honor thursday or both lectures of joint honor (Mon. and Fri.) taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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In this folder you will find the teaching material for Week 6. For hand-written notes for the MTH4215 Single Honours Thursday lecture taught by Dr. Matthew Lewis, please check the QReview as the lectures are demonstrated on the white board.
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Week 7 lectures are arranged to replace the Easter Friday and Monday Holiday breaks.
For example, for MTH4115 (Joint Honor), there will be two lectures (Mon and Fri) at the same time and location. In this folder you will find the teaching material for Week 7. -
Here you can find the teaching material for week 8 and the link to the third quiz.
For hand-written notes for lectures taught by Dr. Matthew Lewis (both lectures for joint honor MTH4115 and thursday lectures for single honor MTH4215), please check the QReview as the lectures are demonstrated on the white board.
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For hand-written notes for lectures taught by Dr. Matthew Lewis (both lectures for joint honor MTH4115 and thursday lectures for single honor MTH4215), please check the QReview as the lectures are demonstrated on the white board.
Here you will find the teaching material for week 9.
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Here you can find the teaching material for week 10 as well as the link for the quiz number 4 which will open on Wednesday March 27th at 2pm and close on Thursday March 28th at 2pm.
Note that due to the Easter holiday, there is only Monday lecture for joint honor MTH4115.
For hand-written notes for the lecture taught by Dr. Matthew Lewis (thursday lectures for single honor MTH4215), please check the QReview as the lectures are demonstrated on the white board. -
Here you can find the teaching material for week 11.Note that due to the Easter holiday, there is only Thurday or Friday lectures for single or joint honor respectively. For hand-written notes for the lecture taught by Dr. Matthew Lewis (thursday lectures for single honor MTH4215), please check the QReview as the lectures are demonstrated on the white board.
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Here you will find the material for revision week.Dr. Matthew Lewis will teach both lectures for single honor (Mon, Thurs); Dr. Weini Huang will teach Monday lecture for joint honor, and Prof. Claudia Garetto will teach the friday lecture for joint honor. Both single and joint lectures will have a revision session in this week, demonstrating parts of the sample exam paper.
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Assessment Pattern - Five in-term assessed online courseworks (4%*5=20%) plus final assessment (80%). This sample exam will be very similar to the format of final assessment 2023/2024.
sample exam paper to be added soom.
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Note this module has been changed and improved over the past years. Thus, the past exam papers should be a good source of practice but not necessarily have the exact format of the final exam in 2023/2024. For a better revision, you should try the questions in the past exams without checking their solutions first. For a concrete format similar to 2023/2024 exam, please follow the sample exam paper to be provided.
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Note this is a sample of randomised online exam. No solution is recorded. The format of this exam is very different from the current exam as well. You can use it to practice questions with similar content but with different format.
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Note this is a sample of randomised online exam. No solution is recorded. The format of this exam is very different from the current exam as well. You can use it to practice questions with similar content but with different format.
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Note this is online exam with multiple choice question. The format of this exam is very different from the current exam as well. You can use it to practice questions with similar content but should be aware it has a very different format.
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