Math 307: Applied Linear Algebra, W19 Term 2, Section 201



The final exam will be held through the Canvas Quiz and it is an OPEN BOOK exam. You can access the lecture notes and the textbook, but not the external online recourses.

The date and time: 8:30 am - 11 am, on April 14th.

The problems are either true/false questions, multiple-choice questions, AND a few short answer questions.

Although it covers everything we learned throughout this term, the final exam is more focused on the material we learned after the midterm.

Chapter 1: Everything except for I.2.4 and I.2.5
Chapter 2: All of II.1, all of II.2 except II.2.3
Chapter 3: All of III.1 except for III.1.5, everthing in III.2, eveything III.3
Chapter 4: All of IV.1 except IV.1.10, IV.2.1-2.4, all of IV.3, IV.4, IV.6.1-6.3, IV.7.1-7.3 and the relationship between the nullspace, range, rank, norms, and SVD.

The homework 6 (no submission) and its solutions are now posted.

The solutions to homework 5 are now posted.

Lecture 34 notes are posted and lecture video is uploaded on Canvas (under the Collaborate Ultra -> Menu -> Recordings).

The homework 5 (not due, no submission) is posted below. Its solutions will be posted soon.

The solutions to homework 4 are now posted.

Past final exams with solutions:
Final 2013 (except problem 5), Another Final 2013 (except problem 5) , Final 2011 (except problem 5)

QUIZ 4 IS ALSO CANCELLED and its weights will be transfered to the final.

I am having office hours from 3 to 5 pm on Mar 20 via Collaborate Ultra on Canvas.

The extended deadline for Homework 4 is Mar 23, Monday. Please submit your homework via Canvas (as a jpg or pdf file).

Lecture 27 notes are posted and lecture video is uploaded on Canvas (under the Media Gallery tab).


Practice problems for Quiz 3 are as follows.
Midterm (2016 W2) : part (f), (g) of problem 1.
Final 2013 : Problem 3,4.
Another Final 2013 : 4.

Homework 4 is now posted (due Mar 20, Friday).

The solutions for midterm are posted.

Office hours for midterm:
Feb 26 (Wednesday) 1-2pm and Feb 27 (Thursday) 1-2pm, both in LSK 300

The midterm exam will cover :
Chapter 1: everything except I.2.4 and I.2.5
Chapter 2: all subsections of II.1 and all subsections of II.2 except II.2.3, II.2.7, II.2.8, and II.2.9

The following problems in the old midterms are on the material covered in Midterm.
Midterm (2016 W2) : Everything except the part 1(g).
Midfterm (2016 W1) : Everything.
Midfterm (2015) : Everything.
Midfterm (2014) : Everthing except the problem 4.

The solutions for the homework 3 are now posted.

The homework 3 (not due, no submission) is posted below. Its solutions will be posted soon.

The solutions for Quiz 2 are uploaded.

The correct solutions for Problem 4 in the assignment 2 are now posted.

The solutions for the assignment 2 are now posted.

Practice problems for Quiz 2 are as follows.
Midfterm (2016 W1) : All parts of problem 4.
Midterm (2016 W2) : Problem 3.
Final 2011 : Problem 2.
Midterm 2015 : Part (a) of problem 3, Problem 4.
Final 2011 : Problem 1, part (a) and (b) of problem 2.

The solutions for Quiz 1 are now posted.

The homework 2 (due Mon, Feb 3) is posted.

The solutions for the first assignments are now posted.

Here are some additional practice problems for Quiz 1.
Midterm (2016 W2) : Problem 1c and Problem 2.
Midfterm (2016 W1) : Problem 1a,c and Problem 2.
Midfterm (2015) : Problem 1 and Problem 2a.
Midfterm (2014) : Problem 1 except part d.

There was a slight change in the lecture note 4.

The first assignment is posted below and it is due on Monday, January 20.

The first lecture will be on Monday, January 6.

Course Information

Lectures: Mon, Wed, Fri 12pm-1pm at room A103, Buchanan.
Course webpage:

Text book: We will use the following online book as the main text.
Chapter 1 : Linear Equations
Chapter 2 : Subspaces, Bases, and Dimension
Chapter 3 : Orthogonality
Chapter 4 : Eigenvalues and Eigenvectors

Instructor Information

Instructor: Halyun Jeong
Office hour: Friday 3-5pm, LSK 300B

Course Outline

Our goal is to cover most of the following topics in the course lecture notes: Interpolation, Finite difference approximations, Formula matrix of a chemical system, Graphs and Networks, Least squres, Fourier series, Fast Fourier Transform, JPEC compression, Power method, Recursion relations, The Anderson tight binding model, Markov chains, Google PageRank.

Grading Policies

The course mark will be deteremined based on homeworks(10%), quizzes(10%), a midterm(30%), and a final(50%).

There will be weekly (sometimes bi-weekly) homework assianments. Please hand in your homework when the class starts on due date. The late homework will not be accepted but the lowest marked homework will be dropped in the final grade calculation. Students are encouraged to discuss homework, but should write up their homeworks individually.

If you miss an assesment (homework, quiz, or midterm) for a valid reason -- see UBC Vancouver Senate's Academic Concession Policy V-135, please fill out an academic request form and bring it to your session instructor. In this case, for a missed homework, the weight will be transferred onto the remaining homework assignment. For a missed quiz, the weight will be transferred to the remaining quizzes, If you miss the midterm, the weight will be transferred onto the final exam. Students will be also expected to provide documentation.

Any student who misses an assessment is to present to their instructor a self-declaration form (or relevant documentation if this is not the first time they miss an assessment) within 72 hours of the assessment date or their mark in the missed assesment will be 0. This policy conforms with the UBC Vancouver Senate's Academic Concession Policy V-135 and students are advised to read this policy carefully.

Computational software support

You will need access to MATLAB software to complete the work for this course. MATLAB is a widely used program for numerical computations with matrices. As of now, MATLAB is available to all UBC students at no cost. For the information including download and activation, follow this link:

You can also access MATLAB in the math department computer lab which is located in LSK 310. The lab hours are posted here. You may use any free terminal in the labs during these times. Your username and password will be given out in the class. Let me know if you have difficulty in login. You may also use GNU Octave and they are also free. However, the instructor will only be able to answer questions regarding MATLAB.

Piazza link for this course

You can ask questions regaring homework, course note, MATLAB,etc. and your instructor, TA, fellow stduents can answer them.

UBC's academic misconduct policies

Exam Information

All exams are closed books and no calculators are allowed.

There will be four in-class quizzes on Jan 22, Feb 5, Mar 18, and Apr 1.

The closed book midterm will be held on Friday February 28, 6:30pm in WESB100.

The final exam date is fixed by UBC (the date/time will be announced soon). Please plan your end-of-term travel carefully according to this date.

Lecture notes and MATLAB scripts

Lecture notes will be uploaded here after each lecture.

Lecture 1 (06/01/2020) : Linear systems with one unknown.

Lecture 2 (08/01/2020) : General systems of linear equations, Gaussian elimination, rref. Matlab script (8/01/2020)

Lecture 3 (10/01/2020) : Vector norms, Matrix norms

Lecture 4 (13/01/2020) : Matrix norm, Condition number

Lecture 5 (17/01/2020) : Condition number Matlab script

Lecture 6 (20/01/2020) : Lagrange interpolation Matlab script

Lecture 7 (22/01/2020) : Splines

Lecture 8 (24/01/2020) : Cubic splines

Lecture 9 (27/01/2020) : Cubic splines

Lecture 10 (29/01/2020) : Cubic splines, Finite difference method

Lecture 11 (31/01/2020) : Finite difference method

Lecture 12 (3/02/2020) : Finite difference method

Lecture 13 (5/02/2020) : Vector space

Lecture 14 (7/02/2020) : Vector spaces, Subspaces

Lecture 15 (10/02/2020) : Subspaces, Linearly independence

Lecture 16 (12/02/2020) : Linearly independence, Span, Bases

Lecture 17 (14/02/2020) : Bases, Four fundamental subspaces of a matrix

Lecture 18 (24/02/2020) : Four fundamental subspaces of a matrix

Lecture 19 (26/02/2020) : Review of four fundamental subspaces, Orthogonality

Lecture 20 (28/02/2020) : Orthogonality

Lecture 21 (2/03/2020) : Orthogonality, Formular matrix for chemical system

Lecture 22 (4/03/2020) : Orthogonal projection

Lecture 23 (6/03/2020) : Orthogonal projection and orthogonal projector

Lecture 24 (9/03/2020) : Orthogonal projection matrices and the least squares problem

Lecture 25 (11/03/2020) : The least squares and Polynomial fitting

Lecture 26 (13/03/2020) : Polynomial fitting, Complex numbers

Lecture 27 (16/03/2020) : Complex numbers

Lecture 28 (18/03/2020) : Complex vectors, Orthogonal basis

Lecture 29 (20/03/2020) : Orthogonal and Unitary matrices

Lecture 30 (23/03/2020) : Eigenvalues and Eigenvectors
Correction: The matrix in the second example with repeated eigenvalues should be [1 1 0; 0 2 0; 0 -1 1].

Lecture 31 (25/03/2020) : Diagonalization, Determinant, and Trace

Lecture 32 (27/03/2020) : Diagonalization, Unitarily Diagonalzation of Hermitian matrices, Power method

Lecture 33 (30/03/2020) : Power method, Recursion relation

Lecture 34 (1/04/2020) : Markov chain

Lecture 35 (3/04/2020) : Google page rank, SVD

Lecture 36 (6/04/2020) : SVD


Homework 1 : Problems 1a, 2, 5, 7, 13, 14 (Due Mon , Jan 20)   Solutions for all problems 1-15 for section 1.1 ,  

Homework 2 (due Mon, Feb 3) : problems 16, 18 in problems_1.1.pdf ,   problems 1, 2, 3, 4 in problems_1.2.pdf
Matlab files for problem 3,4 in problem set 1.2 splinemat2.m , plotcubic2.m , plotspline2.m  
You need to save all these Matlab files in the same working directory or folder which is usually Documents/MATLAB.
Also beware that the function name and its file name should match (such as splinemat2.m, plotcubic2.m, plotspline2.m).

If this is still not working, type "path" command in Matlab command window and save matlab files in one of those working directories.  
Solution for all problems in 1.1 ,   Solution for all problems in 1.2

homework 3 ( No submission. Consider this additional exercise. ) :
problems 1, 2, 3, 4, 5, 6 in problems_1.3.pdf , Matlab files for problem 6 in problem set 1.3 heat.m ,
Solution for Homework 3 (Problem set 1.3)
problems 1, 3, 4, 5, 6, 7 in problems_2.1.pdf Solution for Homework 3 (Problem set 2.1)

homework 4 ( Mar 23, Monday ) :
problems 1 in problems_2.2.pdf (Use Matlab/Octave to solve this problem),
Solution for Homework 4 (Problem set 2.2)
problems 2, 3, 4, 5, 9 in problems_3.1.pdf .
Solution for Homework 4 (Problem set 3.1)

homework 5 ( No submission. Consider this additional exercise. ) :
problems 1, 2ab, 3 in problems_3.2.pdf ,
problems 1, 3, 8, 9 in problems_3.3.pdf ,
Solution for problem set 3.2 ,   Solution for problem set 3.3
problems 1, 2, 3, 4, 5 in problems_4.1.pdf ,
problems 1, 2 in problems_4.2.pdf ,
problems 1, 2 in problems_4.3.pdf ,
Solution for problem set 4.1 ,   Solution for problem set 4.2 ,   Solution for problem set 4.3 ,  

homework 6 ( No submission. Consider this additional exercise. ) :
problems 1, 2 in problems_4.4.pdf ,
problems 1, 2 in problems_4.6.pdf ,
problems 1, 2 in problems_4.7.pdf ,
Solution for problem set 4.4 ,   Solution for problem set 4.6   Solution for problem set 4.7

Exam and Quizzes

Quiz 1 Solution  

Quiz 2 Solution  

Midterm Solutions