Math 218D Fall 2021


Welcome to Math 218D! I will post almost all course materials on this page. Please check back for information about homework assignments, exams, and additional resources. You should probably read the syllabus.

Instructor Email Office Office Hours
Joe Rabinoff Math & Physics 243
M1–3pmLSRC D243
Th3–4pmBioSci 113
Spencer Leslie Math & Physics 222
Jesse Silliman Math & Physics 106
Bowen Li Gross Hall 326
Lecture Instructor Location Time
218D-1 (001) Joe Rabinoff LSRC A247 TTh 12:00–1:15pm
218D-1 (002) Spencer Leslie LSRC A247 TTh 3:30–4:45pm
Problem Session Instructor Location Time
218D-1 (01D) Spencer Leslie Math & Physics 235 F 10:15–11:30am
218D-1 (02D) Jesse Silliman Math & Physics 235 F 12:00–1:15pm
218D-1 (03D) Jesse Silliman Allen 326 F 1:45–3:00pm
218D-1 (04D) Bowen Li Math & Physics 259 F 3:30–4:45pm
218D-1 (05D) Bowen Li Math & Physics 047 F 8:30–9:45am




The official text for the course is Introduction to Linear Algebra (5th Ed) by Gilbert Strang, Wellesley–Cambridge Press/SIAM (2016). However, we will follow Strang only loosely. Another good reference is the online text Interactive Linear Algebra, by Dan Margalit and Joe Rabinoff.


Your first stop for help should be office hours! Joe, Spencer, Jesse, and Bowen will be holding plenty (times listed above), and you should not hesitate to show up with questions and chat with the other students there.

Ask questions on Ed Discussion. Your instructors and fellow students are happy to post answers for everyone to see, and usually do so much more quickly than someone can respond to an email message.

The Math Department operates several Help Rooms to provide assistance to students in lower-level courses. Students are invited to drop by the Help Rooms whenever they are open. No appointment is necessary. If you can't make the scheduled office hours, send us an email and we'll set up a meeting.

The Academic Resource Center (ARC) offers free services to all students during their undergraduate careers at Duke. Services include Learning Consultations, Peer Tutoring, Learning Communities, ADHD/LD Coaching, Outreach Workshops, GRE/MCAT Prep, Study Connect, and more. Because learning is a process unique to every individual, we work with each student to discover and develop their own academic strategy for success at Duke. Contact the ARC to schedule an appointment. Undergraduates in any year, studying any discipline can benefit!


  Topic and Section Materials Homework
Week 1: 8/23 Introduction Joe's Notes
Demo: Best fit ellipse
Demo: Rabbit population
Demo: A Plane
Demo: Two Planes
Homework #1
Due 8/30


Note: Problems 1–22 are about the material in the pre-recorded lecture.
Vectors and Matrices (Ch. 1; 2.4, 2.7)

Recorded: Watch on WarpWire before the second lecture. (If this link doesn't work, use the tab on the Sakai page.)
Joe's Notes and Erratum (fixed in the notes)
Demo: A vector
Demo: Scalar multiplication
Demo: Vector addition
Demo: Vector subtraction
Demo: Linear combinations of two vectors in R2
Demo: Linear combinations of two vectors in R3
Demo: Linear combinations of three vectors in R3
Solving Equations: Elimination (2.2) Joe's Notes
Problem Session Worksheet and Solutions
Week 2: 8/30 Gauss–Jordan Algorithm (2.2, 2.5) Joe's Notes
Gauss–Jordan Slideshow
Rabinoff's Reliable Row Reducer
Homework #2
Updated 9/2
Due 9/6

LU Factorization (2.3, 2.5, 2.6) Joe's Notes
Problem Session Worksheet and Solutions
Week 3: 9/6 Maximal Partial Pivoting; PA=LU (2.6, 2.7) Joe's Notes Homework #3
Updated 9/8
Due 9/13

Parametric Form of Solutions Joe's Notes
Demo: Parameterized Line
Demo: Parameterized Plane
Demo: Column Picture: consistent
Demo: Column Picture: inconsistent
Problem Session Worksheet and Solutions
Week 4: 9/13 Spans (3.2, 3.3) Joe's Notes
Demo: Span of 1 vector in R2
Demo: Span of 2 vectors in R2
Demo: Span of 1 vector in R3
Demo: Span of 2 vectors in R3
Demo: Span of 3 vectors in R3
Demo: Is a vector contained in a span?
Demo: Row/column picture: parallel lines
Demo: Row/column picture: sometimes inconsistent
Homework #4
Due 9/20

Subspaces (3.1, 3.2) Joe's Notes
Demo: Column and Null Space
Problem Session Worksheet and Solutions
Week 5: 9/20 Linear Independence and Basis (3.4, 3.5) Demo: Coplanar vectors
Demo: Redundant parameterization
Demo: Linearly dependent vectors
Demo: Linearly independent vectors
Demo: Linear (In)dependence of 1 vector
Demo: Linear (In)dependence of 2 vectors
Demo: Linear (In)dependence of 3 vectors
Column Rank and Row Rank (3.4, 3.5)  
MIDTERM 1 Practice Midterm
Week 6: 9/27 Orthogonality (3.5, 4.1)    
Orthogonal Decompositions (4.2)  
Problem Session  
Week 7: 10/4 Fall Break  
Projection Matrices (4.2)  
Problem Session  
Week 8: 10/11 Least Squares (4.3)    
Gram–Schmidt and QR (4.4)  
Problem Session  
Week 9: 10/19 Determinants I (5.1, 5.3)    
Determinants II (5.2)  
Week 10: 10/25 Eigenvalues and Eigenvectors (6.1)    
Diagonalization (6.2)  
Problem Session  
Week 11: 11/1 Complex Numbers; Euler's Formula (9.1) Recorded: Watch before first lecture  
AM/GM; Complex Diagonalization (6.2)  
Ordinary Differential Equations I (6.3)  
Problem Session  
Week 12: 11/8 Ordinary Differential Equations II (6.3)    
Spectral Theorem (6.4)  
Problem Session  
Week 13: 11/15 Definiteness; Quadratic Optimization (6.5)    
SVD: Vector Form (7.1, 7.2)  
Week 14: 11/22 SVD: Matrix Form (7.3)    
Week 15: 11/29 SVD: Geometric Meaning (7.4)    
SVD: Application to PCA (7.3)  
Problem Session  
Final exams:
218D-1 (001):Monday, 12/13, 2–5pm
218D-1 (002):Thursday, 12/9, 2–5pm