## Daily Schedule

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
x-hour
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
x-hour
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
x-hour
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
x-hour
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
Rank-nullity worksheet
§4.6: #5, 14, 17
(Th) Oct 19
x-hour
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
x-hour
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
x-hour
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 Gram-Schmidt Process
Gram-Schmidt 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
x-hour
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