See also the course materials in THE SAKAI SYSTEM for some extra video lectures, etc:
The documents, homeworks etc. for the course that we have given/assigned are the below files ordered by date.
Lecture notes from a student's notebook from 2015 Autumn (not complete)
Another lecture notes from a student's notebook (Sinem) from 2013 Autumn (not complete)
Textbook: Linear Algebra: A Geometric Approach, Theodore Shifrin and Malcolm R. Adams. Second edition, W. H. Freeman and Company, 2011.
For the first two weeks of the lectures, study the first chapter from your textbook, Chapter 1 Vectors and Matrices (pages 1-79), solve the problems there and in the following Homework 1; in the lectures, we shall discuss your answers to this HW1 questions, solve them before the lectures so that we can have more time to discuss your answers.
Vectors and Matrices - 1-A - some lecture notes for the 1st week
Video Lecture - 1-A - Vectors and Matrices
Systems of Linear Equations - 1-B - some lecture notes for the 2nd week
Homework 1 - Vectors in the n-Dimensional Space Rn and Systems of Linear Equations (with Worksheet 1 Problems in the last three pages)
See the following article for a simple proof by induction for the uniqueeness of the reduced echelon form of a matrix (you can view this article in the campus network):
Yuster, T. The Reduced Row Echelon Form of a Matrix is Unique: A Simple Proof. Mathematics Magazine, Vol. 57, No. 2 (Mar., 1984), pp. 93-94.
Homework 2 - Matrix Algebra (with Worksheet 2 Problems in the last two pages)
Solve all the problems in the above Homeworks 1 and 2 with the Worksheet Problems in the end and the first two chapters of your textbook. Come to lectures prepared to discuss your answers in the above homework problems.
Your textbook has nice problems to develop your understanding and solving them will make you prepared fully for the midterm and final examinations, you must learn well studying your textbook, it is a nice textbook to learn basics of linear algebra.
Midterm and Final Examinations of the years 2013-2017, 2021-2023
You can find answers to some of these examinations from the faculty photocopy room but I strongly advice you to work hardly to solve them before seeing the answers. You cannot be a problem solver by reading answers to problems.
As a preparation for your midterm, solve the eight midterms in the above set of examinations, you must be able to solve each of them in at most three hours, make yourself these examinations. It will be a good preparation if you can solve all of these eight midterms and understand all the reasoning needed to answer them.
To learn how you shall write your answers, see the detailed answers of the Midterm of 2022 and Midterm of 2023 but of course see the the answers only if you have solved them firstly; you must try to solve them and spent enough time to find the solution, and you must write your answers in a clear way:
Answers to the Midterm of 2022
Answes to the Midterm of 2023
Midterm
We shall discuss the answers to the midterm. To learn how you shall write your answers, see the detailed answers:
Answes to the Midterm
We shall continue with the following topics after the midterm. Solve all the problems in the below Homeworks 3,4 and 5 with the Worksheet Problems in the end and the 3rd, 4th, 5th chapters of your textbook. Come to lectures prepared to discuss your answers in the below homework problems.
Homework 3 - Subspaces of Rn and Dimension (with Worksheet 3 Problems in the last page)
The Four Fundamental Subspaces Associated with a Matrix A (with an example for finding bases for these fundamental subspaces)
Homework 4 - Projections and Linear Transformations (with Worksheet 4 Problems in the last three pages)
Determinants - Lecture notes from a student's notebook from 2015 Autumn (not complete)
Determinants - Geometric Motivation (lecture notes)
Determinants (lecture notes)
Homework 5 - Determinants (with Worksheet 0 Problems)
Answers to Homework 0 - Determinants (in Sakai)
When studying determinants, it will be useful if you know well the sign of permutations in the symmetric group Sn, and even and odd permutations. See the notes The Sign of a Permutation by Keith Conrad (among the many nice Expository Papers).
You shall remember the geometric meaning of determinants from your multivariable calculus; in the Change of Variables Theorem for Multiple Integrals, Jacobian determinant enters the formula. For this viewpoint, see pages 88-130 for determinants from the recently published book Calculus and Analysis in Euclidean Space by Jerry Shurman whose web page also contains many nice notes which are useful for your other courses also. You shall like reading this book to learn rigorously and in a clean way main topics from advanced calculus.
Subjects of the Final Examination
As a preparation for your final examination, solve the eight final examinations in the above set of examinations, you must be able to solve each of them in at most three hours, make yourself these examinations. It will be a good preparation if you can solve all of these eight final examinations and understand all the reasoning needed to answer them.
To learn how you shall write your answers, see the detailed answers of the Final Examination of 2023 but of course see the the answers only if you have solved them firstly; you must try to solve them and spent enough time to find the solution, and you must write your answers in a clear way:
Answers to the Final Examination of 2023