The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
Date  Sections in Text  Description  Practice Problems 

(M) Sep 11  1.1 
Systems of Linear Equations Row reduction slides SageMath plots 
§1.1: #3, 16 
(W) Sep 13  1.2 
Row Reduction and Echelon Forms Row reduction worksheet 
§1.2: #3, 17, 19 
(Th) Sep 14 xhour 
Computing session Sage CoCalc notebook Sage text file 

(F) Sep 15  1.3 
Vector Equations Classwork 
§1.3: #11, 13 
(M) Sep 18  1.4  1.5 
The Matrix Equation Ax=b Solution Sets of Linear Systems 
§1.4: #1, 3, 13 §1.5: #15, 25, 35 
(W) Sep 20  1.7  Linear Independence 
§1.7: #1, 7, 33, 34, 35 
(Th) Sep 21 xhour 
Proofs Methods of proof handout Cheat sheet for proofs 
More proof resources  
(F) Sep 22  1.8 
Introduction to Linear Transformations Linear transformations worksheet, Solutions HW 1 due 3:30 pm 
§1.8: #5, 19, 36 
(M) Sep 25  1.9  The Matrix of a Linear Transformation  §1.9: #11, 21, 27 
(W) Sep 27  2.1  Matrix Operations  §2.1: #5, 12, 22, 26 
(Th) Sep 28 xhour 
Exam 1 review Practice Exam 1, Solutions Practice Exam 2, Solutions 
Past exams 

(F) Sep 29  2.2 
The Inverse of a Matrix HW 2 due 3:30 pm 
§2.2: #15, 31, 37 
(M) Oct 2  2.3  Characterizations of Invertible Matrices  §2.3: #29, 33, 35 
(Tu) Oct 3  Exam 1: 4:30  6:30 pm, Moore Hall B13, Filene Auditorium  
(W) Oct 4  3.1  3.2 
Introduction to Determinants Properties of Determinants 
§3.1: #9, 37 §3.2: #5, 9, 29 
(F) Oct 6  4.1 
Vector Spaces and Subspaces HW 3 due 3:30 pm 
§4.1: #2, 3, 5, 6 
(M) Oct 9  4.2 
Null Spaces (aka Kernels), Column Spaces, and Linear Transformations 
§4.2: #15, 23, 27 
(W) Oct 11  4.3  Linearly Independent Sets and Bases Basis worksheet 
§4.3: #9, 13, 15 
(Th) Oct 12 xhour 
Discussion of solutions to Exam 1  
(F) Oct 13  4.4 
Coordinate Systems Coordinate vector worksheet HW 4 due 3:30 pm 
§4.4: #23, 24, 27 
(M) Oct 16  4.5 
The Dimension of a Vector Space Dimension worksheet 
§4.5: #13, 17, 31 
(W) Oct 18  4.6 
Rank Ranknullity worksheet 
§4.6: #5, 14, 17 
(Th) Oct 19 xhour 
Exam 2 review Practice Exam 1, Solutions Practice Exam 2, Solutions 
Past exams 

(F) Oct 20  4.7 
Change of Basis Change of basis worksheet HW 5 due 3:30 pm 
§4.7: #2, 7, 13 
(M) Oct 23  5.1 
Eigenvectors and Eigenvalues Eigenvector demo Eigenvectors and eigenvalues worksheet 
§5.1: #1, 15, 19 
(Tu) Oct 24 
Exam 2: 4:30  6:30 pm, Moore Hall B13, Filene Auditorium 

(W) Oct 25  5.2  The Characteristic Equation Characteristic polynomial worksheet 
§5.2: #1, 9, 25 
(Th) Oct 26 xhour 
Discussion of solutions to Exam 2  
(F) Oct 27  5.3 
Diagonalization Diagonalization worksheet HW 6 due 3:30 pm 
§5.3: #7, 10, 27 
(M) Oct 30  6.1  Inner Product, Length, and Orthogonality  §6.1: #28, 31 
(W) Nov 1  6.2  Orthogonal Sets Orthogonal sets worksheet 
§6.2: #12, 17, 19 
(Th) Nov 2 xhour 
4.9, 10.1 
Applications to Markov Chains Chapter 10: Markov Chains 
§4.9: #2; §10.2: #15, 17 
(F) Nov 3  6.3 
Orthogonal Projections Orthogonal projections worksheet HW 7 due 3:30 pm 
§6.3: #7, 19, 23 
(M) Nov 6  6.4 
The GramSchmidt Process GramSchmidt worksheet 
§6.4: #9, 15, 19, 20 
(W) Nov 8  7.1 
Diagonalization of Symmetric Matrices Orthogonal diagonalization worksheet 
§7.1: #13, 15, 35 
(Th) Nov 9 xhour 
10.2 
Google's PageRank Chapter 10: Markov Chains PageRank article 
§10.2: #25 
(F) Nov 10  7.4 
Singular Value Decomposition (SVD) SVD worksheet HW 8 due 3:30 pm 
§7.4: #5, 7, 9, 19 
(M) Nov 13  7.5 
Applications of SVD: The Four Fundamental Spaces and Principal Component Analysis (PCA) 

(W) Nov 15 
Review session, 7  9 pm, Kemeny 008 Practice Exam 1, Solutions Practice Exam 2, Solutions 
Past exams Textbook review resources 

(F) Nov 17 
Final Exam: 3:00 pm, Class of 1978 Life Sciences Center, Room 100 