MATH 21-240: Matrix Algebra with Applications

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Course content

Systems of linear equations and their solutions, vectors and matrices, determinants, vector spaces and subspaces, linear independence and bases, orthogonality, dimension, eigenvalues and eigenvectors, linear transformations, Markov chains.

Required text

Linear Algebra and its Applications, Fifth edition by Lay, Lay, and McDonald. Students do not need a physical copy of this book, but are required to purchase an access code to Pearson MyLab Math. This access code will allow you to complete the homework assignments for the course, and also includes an electronic copy of the book.

Schedule

Week 1 (Jan 14-18): Sections 1.1, 1.2, 1.3: systems of linear equations and their solutions, matrices and vectors, row operations.
Week 2 (Jan 21-25): Monday off for MLK day, 1.4, 1.5: first matrix equations, first solution sets of linear systems.
Week 3 (Jan 28-Feb 1): 1.7, 1.8, 1.9: Linear independence, linear transformations, matrices of linear transformations.
Week 4 (Feb 4-Feb 8): 1.6 and 1.10, 2.1, 2.2: Applications, matrix operations, matrix inverses.
Week 5 (Feb 11-Feb 15): 2.3 (characterizations of matrix invertibility), review, exam.
Week 6 (Feb 18-Feb 22): 2.8, 2.9, 4.1: Subspaces with column and null spaces of matrices, dimension and rank, arbitrary vector spaces and subspaces.
Week 7 (Feb 25-March 1): 4.3-4.5, 4.2, 4.6: Bases-coordinates-dimension of vector spaces, null and column spaces, rank
Week 8 (March 4-8): 4.8, 4.9, First day of spring break: applications to difference equations and Markov Chains
Week 9 (March 11-15): SPRING BREAK
Week 10 (March 18-22): 3.1, 3.2, 3.3: Determinants, their properties, Cramer's rule and volumes
Week 11 (March 25-29): 5.1, 5.2, 5.3: Eigenvalues and eigenvectors, the characteristic polynomial, diagonalization
Week 12 (April 1-5): 5.4 (eigenvectors and linear transformations), review, exam
Week 13 (April 8-12): 5.5, 5.7, spring carnival/no class: complex eigenvalues, applications to differential equations
Week 14 (April 15-19): 6.1, 6.2, 6.3: Inner products and length, orthogonal sets, orthogonal projections
Week 15 (April 22-26): 6.4, 6.5, 7.1: Gram-Schmidt, least squares, symmetric matrices
Week 16 (April 29 - May 3): Markov chains, google and baseball, review Final on Tuesday May 7, 8:30 AM, BH A51

Grading

Homework: Homework will count for 30% of the total course grade. Homework is completed online using MyMathLab and there will be an assignment for every section of the text (roughly one assignment per lecture). Each lecture's homework will be posted directly after the lecture, and will be due 6 days later. Late homework will be accepted for up to a week with a 10% penalty.
Quizzes: Students will take a quiz during each recitation section. Quiz grades will make up 10% of the course grade. The lowest 2 quizzes will be dropped.
Exams: There will be two midterm exams, each counting for 15% of the course grade, and a cumulative final counting for 30% of the course grade. There will be no makeup exams, barring serious extenuating circumstances with enough forewarning.

Other course policies

Students are encouraged to work with each other on homework, but the work that is submitted should be completed by the student alone. Students should feel free to consult other textbooks or resources to further understand the course material. You may (and should!) attend any of our office hours for help.

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