Math 341 Winter 2020

Instructor: Robert Lipshitz

Basic course information

Time: MTWF 2:00–2:50 p.m.
Place: 303 Deady Hall.
Textbook: Linear Algebra and Its Applications by David Lay, 5th edition.
Office hours: M 1:00-1:50, M 5:00-6:00, and W 3:00-4:00 in Fenton 303.
Final exam: Per the university Final Exam Schedule
Midterm exams: January 29 and February 1, in class. Subject to change if necessary.
There is also WebWork homework, a Canvas webpage for tracking grades and a blog about using computer software for linear algebra.


Math 252. Math 253 is recommended.

If you are planning to take both this course and Math 281 (multivariable calculus), I recommend taking Math 281 first.

Description and goals

At its heart, linear algebra is about the geometry of systems of linear equations. Linear algebra's importance to both mathematics and its applications rivals—and perhaps exceeds—that of calculus. Unlike calculus, linear algebra becomes clearer in a somewhat abstract setting of vector spaces andlinear transformations. This course is the first in a two-quarter introduction to both concrete and abstract linear algebra.

The main goals of this course are:

  • To provide the first tools from linear algebra needed in mathematics, science and engineering. In this course, those tools include Gauss-Jordan elimination, matrix algebra, and determinants.
  • To introduce abstract vector spaces and linear transformations and the first notions relating to them, including subspaces, bases, dimension, linear independence, and rank.

Specific "learning outcomes" include being able to find the solutions of a system of linear equations and understand the geometric meaning of the space of solutions; understanding the notions of a subspace, basis, and dimension, finding bases, and computing dimensions; understanding how to represent vectors with respect to different bases; understanding the definitions of linear transformations, some basic examples, and how to write linear transformations in terms of matrices; being able to find bases for the kernel and image of a linear transformation; and being able to compute determinants.



Written homework 20%
Online homework 10%
Midterm 1 20%
Midterm 2 20%
Final 30%



The course will have both written and online homework. Written homework is due at the beginning of class on Wednesdays, except as noted. Online homework, via WebWorks, is due before class on Mondays, except as noted. (Due dates may change.) You may work together on homework assignments, get help from tutors or other students, or get general help from online websites, but you may not use websites or other resources that post exact solutions to problems on the assignment. All resources you use except the textbook must be cited on your assignment. This includes help from your classmates, friends, or online resources. Failure to cite sources constitutes plagiarism, a serious form of academic dishonesty, and will be punished. Copying solutions from any source (online, friend, etc.) is academic misconduct, and will be referred to the university for discipline.

You may work together on homework assignments, but you must write up the final version of your answers by yourself. Again, working on the final write-ups together constitutes cheating.

Late homeworks will not be accepted, but the lowest written homework score and lowest online homework score will be dropped.

The WebWork homework site, for online homework, is Written homework assignments are posted below.

A small number of bonus points -- a maximum of 5% of the score on each homework assignment -- will be awarded for following the tutorial on using CoCalc alongside the class.


All exams will be given in class, and there will typically not be makeup exams. If you know in advance that you will miss an exam, contact me immediately to make arrangements. If you miss an exam because of an emergency (medical, family, ...) you will be expected to provide documentation of that emergency.

All exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). Using any notes or electronic device or communicating with anyone except me during an exam constitutes cheating.

Students with disabilities

I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center. Setting up accomodations takes time; it is your responsibility to contact the AEC promptly.

Written homework

Again, all written homework is due at the beginning of class on the due date.


This schedule is tentative, and may change during the quarter.

01/06 - 01/10 Systems of linear equations, row-reduced echelon form 1.1, 1.2, 1.3  
01/13 - 01/17 Matrix-vector product, solution sets, applications. Linear independence. 1.4, 1.5, 1.6, 1.7  
01/20 - 01/24 More linear independence, linear transformations 1.7, 1.8, 1.9 January 20 is a holiday.
01/27 - 01/31 Applications of linear transformations, review, midterm. Matrix multiplication. 1.10, 2.1 Midterm 1 on Wednesday, January 29.
02/03 - 02/07 Inverses, matrix factorizations 2.2, 2.3, 2.4, 2.5  
02/10 - 02/14 Subspaces of Rn. Determinants 2.8, 2.9, 3.1  

02/17- 02/21

More determinants. Review, midterm. 3.2, 3.3 Midterm 2 on Friday, February 21
02/24 - 02/28 Vector spaces, subspaces. Null space, column space. 4.1, 4.2  
03/02 - 03/06
Linear independence, bases. Dimension. 4.3, 4.4, 4.5  
03/09 - 03/13 Rank, change of basis. Review. 4.6, 4.7  



Handouts will be posted here, in case you lost the physical copy.


Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.

Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles, but if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours. The Teaching and Learning Center also facilitates individual and small-group tutoring.

Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.