Mat 342 (Linear Algebra, Course #71354), Fall 2017



Course Information
Instructor Class Times Office Hours
Evan Dummit
edummit at asu dot edu
MWF 2:00pm-2:50pm
Wexler A107
T 1:15pm-2:15pm
W 12:45pm-1:45pm
F 3:00pm-4:00pm
Wexler 744
For detailed information about the course, please consult the 342 Course Syllabus.
The WebWork assignments in this course are available on the 342 WebWork Page, while the written homework assignments will appear here. Some Tips on Problem Solving are available as suggestions for the written assignments.
The instructor will write lecture notes for the course (see below) in lieu of an official textbook as the semester progresses. The course will generally follow the presentation in Leon's “Linear Algebra With Applications” (9th edition), but it is not necessary to purchase the textbook for this course.


Written Homeworks
Written Homework #1, due Wed September 13th. (solutions)

Written Homework #2, due Wed October 4th. (solutions)

Written Homework #3, due Wed October 18th. (solutions)

Written Homework #4, due Mon November 13th. (solutions)

Written Homework #5, due Fri December 1st.


Handouts / Lecture Notes
Handout Topics
Chapter 1: Matrices and Systems of Linear Equations (20pp, v2.60, updated 8/26) (changes in 2.60: fixed chapter numbering, expanded examples in 1.1.2) 1.1 ~ Systems of Linear Equations
1.2 ~ Matrix Operations: Addition and Multiplication
1.3 ~ Determinants and Inverses
1.4 ~ Matrices and Systems of Linear Equations, Revisited
Chapter 2: Vector Spaces (26pp, v2.60, updated 9/25)
(changes in 2.60: deleted duplicate material in section 2.5.3, moved other material to 2.5.1, fixed typos)
2.1 ~ Vectors in Rn
2.2 ~ The Formal Definition of a Vector Space
2.3 ~ Subspaces
2.4 ~ Linear Combinations and Span
2.5 ~ Linear Independence and Linear Dependence
2.6 ~ Bases and Dimension (Existence, Properties, Computation)
Chapter 3: Inner Products (16pp, v2.50, posted 10/4) 3.1 ~ Inner Products
3.2 ~ Orthogonality
3.3 ~ Applications of Inner Products
Chapter 4: Linear Transformations (17pp, v2.60, updated 11/2)
(changes in 2.60: added proposition on properties of invertible matrices and shift operator example to end of 4.4.2)
4.1 ~ Linear Transformations
4.2 ~ Kernel and Image
4.3 ~ Isomorphisms of Vector Spaces
4.4 ~ Matrices Associated to Linear Transformations (Definition, Properties, Change of Basis)
Chapter 5: Eigenvalues and Diagonalization (22pp, v2.50, posted 11/2) 5.1 ~ Eigenvalues, Eigenvectors, Eigenspaces
5.2 ~ Diagonalization
5.3 ~ Applications of Diagonalization
Appendix: Complex Numbers (5pp, v2.50, posted 9/6) A.1 ~ Arithmetic with Complex Numbers
A.2 ~ Complex Exponentials, Polar Form, and Euler's Theorem


Exam Information
Exam Date, Time, Location Topics Review Material
Midterm 1
(Exam) (Solutions)
Wed, September 20th
In Lecture, 2:00-2:50pm
Notes §1.1-1.4 + §2.1-2.3
WebWork 1-4 + Written HW 1
Midterm 1 Review Problems
Review session 4:30-6pm Tue 9/19, Wexler A106
Midterm 2
(Exam) (Solutions)
Mon, October 23rd
In Lecture, 2:00-2:50pm
Notes §2.4-2.6 + §3.1-3.2
WebWork 5-8 + Written HW 2-3
Midterm 2 Review Problems
Review session 2:30-4:30pm Sun 10/22, Wexler A106
Midterm 3
(Exam) (Solutions)
Fri, November 17th
In Lecture, 2:00-2:50pm
Notes §4.1-4.4, §5.1
WebWork 9-10 + Written HW 4
Midterm 3 Review Problems
Review session 5:30-7pm Thu 11/16, Wexler A306
Final Mon, December 4th
TBA, 2:30-4:20pm
Notes §1.1-5.2
WebWork 1-11 + Written HW 1-5
Final Review Problems
Review session TBA
Bring your University ID to all exams. Calculators, cell phones, other electronic devices, books, and notes of any kind will NOT be permitted in exams.


How to Get Extra Help
Attend Lecture Missing lecture is a bad idea! If for any reason you cannot make it to a class, you should review notes from someone who did attend. You are responsible for all material covered in lecture.
Read the Lecture Notes The lecture notes are intended as review material, although many students like to read them as preparation before attending the lecture on the corresponding topics. Please note that the electronic notes will not always be identical to the material covered in class: this is by design, so as to provide you a slightly different perspective on the material.
Ask Questions Via WebWork On each WebWork problem's page, there is an "Email Instructor" button at the bottom. If you are having difficulty with a problem (if you are stuck or you believe there is an error or issue with the problem) you can ask a question at any time, and the TA or instructor will typically respond within 24 hours, if not sooner.
Attend Office Hours Office hours are specifically reserved for you to receive individual, one-on-one help from the instructor. Office hours will be the most effective when you have already put in effort to learn the material on your own (including trying to solve the homework problems), and when you come in with a list of specific questions or topics you are struggling with.
Tutoring The university offers a wide variety of free tutoring services both online and in-person. Please consult the ASU Tutor Search page for additional information. It is also possible to hire private tutors, some of whom are listed here.
Math Community Center The Math Community Center is located in Wexler 303 and staffed by faculty and graduate students Mon-Fri, typically 10:30am-6pm. It is a common location intended for students to collaborate and have peer mentoring sessions, and also provides structured course assistance from graduate-student tutors.


Course Schedule
The schedule is subject to change!
Week Schedule
Week of Aug 14
(class starts 8/18)
§1.1.1: Systems of Linear Equations
No homework this week
Week of Aug 21 §1.1.2: Row-Echelon Form and Reduced Row-Echelon Form
§1.1.3: Gaussian Elimination
§1.2: Matrix Operations
WebWork 1 due Saturday 8/26 at 6am.
Week of Aug 28 §1.2: Matrix Operations
§1.3.1: The Inverse of a Matrix
§1.3.2: The Determinant of a Matrix
WebWork 2 due Saturday 9/2 at 6am.
Week of Sep 4
(no class 9/4)
§1.3.3: Cofactor Expansions and the Adjugate
§1.4: Systems of Linear Equations, Revisited
WebWork 3 due Saturday 9/9 at 6am.
Week of Sep 11 §2.1: Vectors in Rn
§2.2: The Formal Definition of a Vector Space
§2.3: Subspaces
Written Homework 1 due Wednesday 9/13 in lecture.
Week of Sep 18 Review for Midterm 1
WebWork 4 due Tuesday 9/19 at 6am.
Review session for Midterm 1 Tuesday 9/19 from 4:30-6:00pm in Wexler A106
MIDTERM 1 in class Wednesday 9/20
§2.4: Linear Combinations and Span
Week of Sep 25 §2.5: Linear Independence and Linear Dependence
§2.6.1: Bases of Vector Spaces
§2.6.2: Existence of Bases
WebWork 5 due Saturday 9/30 at 6am.
Week of Oct 2 §2.6.3: Dimension
§2.6.4: Finding Bases, Rowspaces, Column Spaces, and Nullspaces
§3.1: Inner Products
Written Homework 2 due Wednesday 10/4 in lecture.
WebWork 6 due Saturday 10/7 at 6am.
Week of Oct 9
(no class 10/9)
§3.2.1: Orthogonality
§3.2.2: Orthonormal Bases and the Gram-Schmidt Procedure
WebWork 7 due Saturday 10/14 at 6am.
Week of Oct 16 §3.2.3: Orthogonal Projection
§3.3: Applications of Inner Products (Least-Squares, Fourier Series)
Written Homework 3 due Wednesday 10/18 in lecture.
Review for Midterm 2
WebWork 8 due Saturday 10/21 at 6am.
Week of Oct 23 MIDTERM 2 in class Monday 10/23
§4.1: Linear Transformations
§4.2: Kernel and Image
No homework this week
Week of Oct 30 §4.3: Isomorphisms of Vector Spaces
§4.4.1: Matrices Associated to Linear Transformations
§4.4.2: Algebraic Properties of Associated Matrices
WebWork 9 due Saturday 11/4 at 6am.
Week of Nov 6
(no class 11/10)
§4.4.3: Change of Basis and Similarity
§5.1.1: Eigenvalues and Eigenvectors
WebWork 10 due Saturday 11/11 Tuesday 11/14 at 6am.
Week of Nov 13 Written Homework 4 due Monday 11/13 in lecture.
§5.1.2: Eigenvalues and Eigenvectors of Matrices
§5.1.3: Eigenspaces
Review for Midterm 3
MIDTERM 3 in class Friday 11/17
Week of Nov 20
(no class 11/24)
§5.2: Diagonalization
No homework this week
Week of Nov 27 §5.2: Diagonalization
§5.3: Applications of Diagonalization
Review for Final Exam
Written Homework 5 due Friday 12/1 in lecture.
WebWork 11 due Sunday 12/3 at 6am.
FINAL EXAM Monday 12/4, 2:30-4:20pm, location TBA