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  Office Hours  

Joe Rabinoff  jdr@math.duke.edu  Math & Physics 243 


Spencer Leslie  lesliew@math.duke.edu  Math & Physics 222 


Jesse Silliman  jesse.silliman@duke.edu  Math & Physics 106 


Bowen Li  bowen.li200@duke.edu  Gross Hall 326 

Lecture  Instructor  Location  Time 

218D1 (001)  Joe Rabinoff  LSRC A247  TTh 12:00–1:15pm 
218D1 (002)  Spencer Leslie  LSRC A247  TTh 3:30–4:45pm 
Problem Session  Instructor  Location  Time 
218D1 (01D)  Spencer Leslie  Math & Physics 235  F 10:15–11:30am 
218D1 (02D)  Jesse Silliman  Math & Physics 235  F 12:00–1:15pm 
218D1 (03D)  Jesse Silliman  Allen 326  F 1:45–3:00pm 
218D1 (04D)  Bowen Li  Math & Physics 259  F 3:30–4:45pm 
218D1 (05D)  Bowen Li  Math & Physics 047  F 8:30–9:45am 
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, 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 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 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 11:59pm Note: Problems 1–22 are about the material in the prerecorded 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 R^{2} Demo: Linear combinations of two vectors in R^{3} Demo: Linear combinations of three vectors in R^{3} 

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 11:59pm 

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 11:59pm 

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 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: Is a vector contained in a span? Demo: Row/column picture: parallel lines Demo: Row/column picture: sometimes inconsistent 
Homework #4 Due 9/20 11:59pm 

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) 
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 
Homework #5 Due 9/29 11:59pm 

Column Rank and Row Rank (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 

MIDTERM 1 
Practice Midterm
and Solutions Midterm and Solutions 

Week 6: 9/27  Orthogonality (3.5, 4.1) 
Joe's Notes Demo: Closest vector to b Demo: An orthogonal complement in R^{3} Demo: An orthogonal complement in R^{3} Demo: Orthogonal complements in R^{2} 
Homework #6 Due 10/6 11:59pm 

Orthogonal 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: 10/4  Fall Break 
Homework #7 Due 10/11 11:59pm 

Projection Matrices (4.2) 
Joe's Notes 

Problem Session  Worksheet and Solutions  
Week 8: 10/11  Least Squares (4.3) 
Joe's Notes Demo: LeastSquares Demo: Bestfit line Demo: Bestfit parabola Demo: Bestfit trigonometric function Demo: Bestfit ellipse Demo: Bestfit ellipse: what is minimized? 
Homework #8 Due 10/18 11:59pm 

Gram–Schmidt and QR (4.4) 
Joe's Notes 

Problem Session  Worksheet and Solutions  
Week 9: 10/19  Determinants I (5.1, 5.3)  Joe's Notes 
Homework #9 Updated 10/24 Due 10/27 11:59pm 

Determinants II (5.2) 
Joe's Notes Supplement: cofactor matrix 

MIDTERM 2 
Practice Midterm
and Solutions Midterm and Solutions 

Week 10: 10/25  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 
Homework #10 Due 11/3 11:59pm 

Diagonalization (6.2) 
Joe's Notes 

Problem Session  Worksheet and Solutions  
Week 11: 11/1 
Complex Numbers; Euler's Formula (9.1) Recorded: Watch on WarpWire before Tuesday's lecture. (If this link doesn't work, use the tab on the Sakai page.) 
Joe's Notes 
Homework #11 Due 11/8 11:59pm 

Complex Diagonalization (6.2) 
Joe's Notes Dynamics demos: 

AM/GM; Ordinary Differential Equations I (6.3) 
Joe's Notes Demo: Eigenspaces of a nondiagonalizable 3x3 matrix Demo: Eigenspaces of a diagonalizable 3x3 matrix 

Problem Session  Worksheet and Solutions  
Week 12: 11/8  Ordinary Differential Equations II (6.3)  Joe's Notes 
Homework #12 Updated 11/11 Due 11/15 11:59pm 

Spectral Theorem (6.4) 
Joe's Notes Demo: Eigenspaces of a 3x3 symmetric matrix Demo: Dynamics of a 2x2 symmetric matrix 

Problem Session  Worksheet and Solutions  
Week 13: 11/15  Quadratic Optimization (6.5)  Joe's Notes 
Homework #13 Due 11/24 11:59pm 

Quadratic Optimization continued; LDL^{T} 
Joe's Notes Supplement: LDL^{T} and Cholesky 

MIDTERM 3 
Practice Midterm
and Solutions Midterm and Solutions 

Week 14: 11/22  SVD (7.1–7.3) On Zoom (see Sakai announcements). 
Joe's Notes 
Homework #14 Due 12/1 11:59pm 

Thanksgiving  
Thanksgiving  
Week 15: 11/29  SVD: Matrix Form (7.3) 
Joe's Notes 
Homework #15 (Not collected) 

SVD: Application to PCA (7.3) 
Joe's Notes 

Problem Session  
Final exams:

Practice Final and Solutions 