Math 218D-1 Fall 2023


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.

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Joe Rabinoff
Joe Rabinoff

Joe Rabinoff
Math & Physics 243
Office Hours:
Tu1–2pmMath & Physics 274J
W10–noomMath & Physics 274J
Eylem Yildiz
Eylem Yildiz

Eylem Yildiz
Math & Physics 114
Office Hours:
Tu4:30–6pmMath & Physics 113
Th4:30–6pmMath & Physics 113
Rohit Kumar
Rohit Kumar

Rohit Kumar
Office Hours:
Tu3–5pmGross Hall 351
Wnoon–1pmGross Hall 351
Dante Bonolis
Dante Bonolis

Dante Bonolis
Office Hours:
Tu5–7pmMath & Physics 101
W5–6pmGross Hall 104
Linda Wang
Linda Wang

Linda Wang
Office Hours:
M10–11:20amMath & Physics 274J
Tu10–11:30amMath & Physics 274J


Lecture Instructor Location Time
218D-1 (001) Joe Rabinoff Math & Physics 154 TTh 11:45am–1:00pm
218D-1 (002) Eylem Yildiz Math & Physics 130 TTh 3:05–4:20pm
Problem Session Instructor Location Time
218D-1 (01D) Rohit Kumar Allen 326 F 10:05–11:20am
218D-1 (02D) Rohit Kumar Reuben-Cooke 127 F 11:45am–1:00pm
218D-1 (03D) Dante Bonolis Reuben-Cooke 127 F 1:25–2:40pm
218D-1 (04D) Dante Bonolis Reuben-Cooke 127 F 3:05–4:20pm
218D-1 (05D) Eylem Yildiz Reuben-Cooke 127 F 8:30–9:45am


Access Gradescope by clicking on the tab in Sakai.


Strang, Introduction to Linear Algebra
The official text for the course is Introduction to Linear Algebra (6th 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.


Office Hours
Your first stop for help should be office hours! Joe, Eylem, Rohit, Dante, and our undergraduate TA Linda will be holding plenty (times listed above), and you should not hesitate to show up with questions and chat with the other students there.
Ed Discussion
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.
SAGE Learning Communities
The STEM Advancement Through Group Education (SAGE) program is a resource offered in conjunction with the Academic Resource Center. These groups meet weekly with a trained undergraduate Peer Facilitator and engage with content closely correlated with the course. SAGE students are highly motivated, want to establish a critical foundation for STEM learning at Duke, and are interested in learning in a community with other students. SAGE helps students learn effective STEM study strategies, provides extra support for the challenging material in the course, and fosters a collaborative community of learners. Sign-ups will begin after the drop/add period. Information about how to sign up and more details about the program can be found here.
The Academic Resource Center
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: 8/28 Introduction Joe's Notes
Demo: Best fit ellipse
Demo: Rabbit population
Demo: A Plane
Demo: Two Planes
Homework #1
Due 9/6

Note: HW#1 also covers the recorded lecture.
Vectors and Matrices (Ch. 1, 2.4, 2.7) Joe's Notes

Recorded: Watch on WarpWire (on Sakai) before the second lecture.
Solving Equations: Elimination (2.2) Joe's Notes
Problem Session
Week 2: 9/4 Gauss–Jordan Algorithm (2.2, 2.5) Joe's Notes
Gauss–Jordan Slideshow
Rabinoff's Reliable Row Reducer
Homework #2
Due 9/13

LU Decomposition (2.3, 2.6) Joe's Notes
Problem Session Quiz
Week 3: 9/11 Parametric Form Joe's Notes
Demo: Parameterized Line
Demo: Parameterized Plane
Homework #3
Due 9/20

Spans (3.2, 3.3) Joe's 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
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: Column Picture for Consistency: Consistent
Demo: Column Picture for Consistency: Inconsistent
Demo: Row/column picture: parallel lines
Demo: Row/column picture: sometimes inconsistent
Problem Session Quiz
Week 4: 9/18 Subspaces (3.1, 3.2) Joe's Notes
Demo: Column and Null Space
Homework #4
Due 9/27

Linear Independence and Basis (3.4, 3.5) Joe's Notes
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
Demo: Linear Dependence of 3 vectors in R2
Problem Session Quiz
Week 5: 9/25 Fundamental Subspaces (3.4, 3.5) Joe's Notes
Demo: Rank-nullity: n=3, r=0
Demo: Rank-nullity: n=3, r=1
Demo: Rank-nullity: n=3, r=2
Demo: Rank-nullity: n=3, r=3
Homework #5
Due 10/4

Orthogonal Complements (3.5, 4.1) Joe's Notes
Demo: Closest vector to b
Demo: Orthogonal complement of one vector
Demo: Orthogonal complement of two vectors
Demo: Orthogonal complements in R2
Problem Session
Week 6: 10/2 Orthogonal Projections (4.2) Joe's Notes
Demo: Decomposition relative a line in R2
Demo: Decomposition relative a line in R3
Demo: Decomposition relative a plane in R3
Demo: Projection onto a plane
Demo: Projection onto a line
Demo: Projection onto a plane
Homework #6
Due 10/11

Projection Matrices (4.2) Joe's Notes
Friday, 10/6: MIDTERM 1 Practice Midterm and Solutions
Midterm and Solutions
Week 7: 10/9 Least Squares (4.3) Joe's Notes
Demo: Least-Squares
Demo: Best-fit line
Demo: Best-fit parabola
Demo: Best-fit trigonometric function
Demo: Best-fit ellipse
Demo: Best-fit ellipse: what is minimized?
Homework #7
Due 10/19

Gram–Schmidt and QR (4.4) Joe's Notes
Demo: Projection formula
Problem Session
Week 8: 10/16 FALL BREAK Homework #8
Due 10/25

Determinants I (5.1, 5.3) Joe's Notes
Problem Session
Week 9: 10/23 Determinants II (5.2) Joe's Notes
Supplement: cofactor matrix
Homework #9
Due 11/1

Eigenvalues and Eigenvectors (6.1) Joe's Notes
Demo: Rabbits Multiply
Demo: Eigenspaces of a flip
Demo: Eigenspaces of a shear
Demo: Eigenspaces of a rotation
Demo: Eigenspaces of the rabbit matrix
Demo: Eigenspaces of a 3x3 matrix
Demo: Eigenspaces of a projection matrix
Problem Session
Week 10: 10/30 Diagonalization: Vector Form (6.2) Joe's Notes Homework #10
Due 11/8

Diagonalization: Geometry (6.2) Joe's Notes
Dynamics demos:
Problem Session
Week 11: 11/6 Complex Numbers; Euler's Formula (9.1) Joe's Notes

Recorded: Watch on WarpWire (on Sakai) before Tuesday's lecture.
Homework #11
Due 11/15

AM/GM and Diagonalizability (6.2) Joe's Notes
Supplement: Proof of the AM≥GM theorem

AM/GM demos:
Dynamics with a Complex Eigenvalue
Systems of ODEs (6.3) Joe's Notes
Friday, 11/10: MIDTERM 2 Practice Midterm and Solutions
Midterm and Solutions
Week 12: 11/13 Spectral Theorem (6.4) Joe's Notes
Demo: Eigenspaces of a 3x3 symmetric matrix
Demo: Eigenspaces of a 3x3 symmetric matrix (GM=2)
Demo: Dynamics of a 2x2 symmetric matrix
Homework #12
Due 11/22

LDLT; Quadratic Optimization (2.7, 6.5) Joe's Notes
Supplement: LDLT and Cholesky
Problem Session
Week 13: 11/20 Quadratic Optimization II (6.5) Joe's Notes Homework #13
Due 11/29

Week 14: 11/27 SVD: Outer Product Form (7.1, 7.2) Joe's Notes Homework #14
Due 12/6

SVD: Matrix Form (7.3) Joe's Notes
Problem Session
Week 15: 12/4 PCA I (7.3, 7.4) Joe's Notes Homework #15
(Not collected)

PCA II (7.3) Joe's Notes
Problem Session
Final exams:
218D-1 (001):Friday, 12/15, 2–5pm
218D-1 (002):Friday, 12/15, 7–10pm
Practice Final and Solutions