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  Office Hours  

Joe Rabinoff  jdr@math.duke.edu 


Jesse Silliman  jesse.silliman@duke.edu 

Lecture  Instructor  Time 

218D001  Joe Rabinoff  MW 12:00–12:50pm 
218D002  Joe Rabinoff  TTh 3:30–4:20pm 
Problem Session  Instructor  Time 
218D01D  Jesse Silliman  F 10:15–11:05am 
218D02D  Jesse Silliman  F 12:00–12:50pm 
218D03D  Jesse Silliman  F 1:45–2:35pm 
218D04D  Jesse Silliman  F 3:30–4:20pm 
218D05D  Joe Rabinoff  M 10:15–11:05am 
Links:
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 and Jesse 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 Piazza! Your instructors and fellow students are happy to post answers for everyone to see.
The Math Department operates several Help Rooms to provide assistance to students in lowerlevel 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.
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Topic  Materials  Remarks  Homework  

Week 1: 8/17 
Vectors and Matrices (Ch. 1; 2.4) 
Joe's Notes Demo: A vector Demo: Scalar multiplication Demo: Vector addition Demo: Vector subtraction Demo: Linear combos in R^{2} Demo: Linear combos in R^{3} Demo: Linear combos in R^{3} 
Prerecorded: watch here before the second lecture 
HW#1 Due 8/25 11:59pm Note: Problems 1–21 are about the material in the prerecorded lecture. 
Introduction 
Joe's Notes Jesse's Notes Demo: Best fit ellipse Demo: Rabbit population Demo: A Plane Demo: Two Planes 

Elimination (2.2) 
Joe's Notes Jesse's Notes 

Problem Session  Worksheet and Solutions  
Week 2: 8/24 
Gauss–Jordan (2.2) 
Joe's Notes Jesse's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer 
HW#2 Due 9/1 11:59pm 

LU Factorization (2.3, 2.5, 2.6, 2.7) 
Joe's Notes Jesse's Notes 
Supplement: PA=LU  
Problem Session  Worksheet and Solutions  
Week 3: 8/31 
Parametric Form 
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane Demo: Column Picture: consistent Demo: Column Picture: inconsistent 
HW#3 Due 9/8 11:59pm 

Vector Equations (2.1, 3.2, 3.3) 
Joe's Notes Demo: Span of 1 vector in R^{2} Demo: Span of 2 vectors in R^{2} Demo: Span of 1 vector in R^{3} Demo: Span of 2 vectors in R^{3} Demo: Span of 3 vectors in R^{3} Demo: Row/col picture: full row rank Demo: Row/col picture: not full row rank 

Problem Session  Worksheet and Solutions  
Week 4: 9/7 
Transposes (2.7), Rank (3.2), Subspaces (3.1, 3.2)  Joe's Notes 
HW#4 Due 9/17 11:59pm 

Subspaces (3.1, 3.2, 3.3) 
Joe's Notes Demo: Column and Null Space 

Problem Session  Worksheet and Solutions  
Week 5: 9/14 
Tuesday, 9/15: Midterm 1 
Practice Midterm
and Solutions Midterm and Solutions 
HW#5 Due 9/22 11:59pm 

Linear Independence (3.4) 
Joe's Notes Demo: Coplanar vectors Demo: Lin. (In)dep. of 1 vector Demo: Lin. (In)dep. of 2 vectors Demo: Lin. (In)dep. of 3 vectors 

Basis and Dimension (3.4, 3.5) 
Joe's Notes Demo: Ranknullity: n=3, r=0 Demo: Ranknullity: n=3, r=1 Demo: Ranknullity: n=3, r=2 Demo: Ranknullity: n=3, r=3 
Supplement: full rank matrices  
Problem Session  Worksheet and Solutions  
Week 6: 9/21 
Orthogonality (4.1) 
Joe's Notes Demo: Ortho complements in R^{2} Demo: Ortho complements in R^{3} Demo: Ortho complements in R^{3} 
HW#6 Due 9/29 11:59pm 

Projections (4.2) 
Joe's Notes Demo: Projection onto a line Demo: Projection onto a plane Demo: Decomp. relative a line Demo: Decomp. relative a plane 

Problem Session  Worksheet and Solutions  
Week 7: 9/28 
Least Squares (4.3) 
Joe's Notes Demo: LeastSquares Demo: Bestfit line Demo: Bestfit parabola 
See ILA for other leastsquares examples. 
HW#7 Due 10/6 11:59pm 
Gram–Schmidt (4.4) 
Joe's Notes Demo: Projection Formula 

Problem Session  Worksheet and Solutions  
Week 8: 10/5 
Determinants I (5.1, 5.3) 
Joe's Notes 
HW#8 Due 10/15 11:59pm 

Determinants II (5.2) 
Joe's Notes 
Supplement: cofactor matrix  
Problem Session  Worksheet and Solutions  
Week 9: 10/12 
Tuesday, 10/13: Midterm 2 
Practice Midterm
and Solutions Midterm and Solutions 
HW#9 Due 10/20 11:59pm 

Eigenvalues (6.1) 
Joe's Notes Demo: Rabbits Multiply Demo: Eigenspaces of a 2x2 Demo: Eigenspaces of a 3x3 Demo: Eigenspaces of a projection Demo: Eigenspaces of a rotation Demo: Eigenspaces of a shear 

Diagonalization (6.2)  Joe's Notes 

Problem Session  Worksheet and Solutions  
Week 10: 10/19 
Complex Numbers (9.1)  Joe's Notes 
Prerecorded; watch before the first lecture 
HW#10 Due 10/27 11:59pm 
Complex Diagonalization (6.2) 
Joe's Notes Dynamics demos: 

ODEs (6.3)  Joe's Notes  
Problem Session  Worksheet and Solutions  
Week 11: 10/26 
Spectral Theorem (6.4) 
Joe's Notes Demo: Eigenspaces of a symmetric matrix 
HW#11 Due 11/5 11:59pm 

Quadratic Forms (6.5) 
Joe's Notes 
Supplement: LDL^{T} and Cholesky  
Problem Session  Worksheet and Solutions  
Week 12: 11/2 
SVD I (7.1, 7.2)  Joe's Notes 
HW#12 Due 11/12 11:59pm 

SVD II (7.2)  Joe's Notes  
Problem Session  Worksheet and Solutions  
Week 13: 11/9 
Geometry of the SVD (7.4)  Joe's Notes 
HW#13 (Not collected) 

SVD and PCA (7.3)  Joe's Notes  
Problem Session  
Monday, 11/16: Midterm 3 
Practice Midterm
and Solutions Midterm and Solutions 

Monday, 11/23, 2–5pm / Tuesday, 11/24, 2–5pm: Final Exam 
Practice Final and Solutions 