# Linear Algebra - Summer II 2012

## Office Hours

Office: 607 at Warren Weaver Hall (251 Mercer Street).
Schedule: T,W 11:05-12:05

## Course Objectives

Upon successfully completing this course students will be able to:

• Formulate, solve, apply, and interpret systems of linear equations in several variables;
• Compute with and classify matrices;
• Demonstrate elementary facts in abstract vector spaces;
• Decompose linear transformations according to their spectra (eigenvectors and eigenvalues)
• Use length and orthogonality in each of the above contexts.

## Resources

Text: Linear Algebra and its Applications by David C. Lay (4th ed., Addison-Wesley, 2005. ISBN 978-0321287137). New and used copies are on sale in the NYU Bookstore and can also be found online, check here and here. A copy will be put on reserve in Bobst Library, check here.

Calculator Policy: Calculators may not be used on quizzes or exams, and will be of little or no help with homework.

## Evaluation

There will be regular homework, periodic quizzes, a midterm exam and a final exam. These elements will be combined into a course average using the weights by each category below.

• Homework (20%): Homework will be assigned everyday, and its due at the beginning of the following lecture. I encourage you to work in groups, but the work must be your own in the end. Check the schedule section to check out the problem list of each day. The lowest 2 homework scores will be dropped.

• Quiz (20%): There will be four ~30-min quizzes, July 5, 12, 27 and August 2. For more details check the schedule. The lowest quiz score will be dropped.

• Midterm (25%): An in-class midterm, July 20.

• Final (35%): An in-class final, August 10.

Policy on special circumstances: In general, late homework assignments will not be accepted, and quizzes cannot be rescheduled. However, I will drop the lowest 2 homework scores, no excuses necessary. Makeup exams or quizzes will be offered only in the following cases:

• A documented medical excuse.
• A University-sponsored event such as an athletic tournament, a play, or a musical performance. Athletic practices and rehearsals do not fall into this category. Please present documentation from your coach, conductor, or other faculty advisor describing your absence.
• A religious holiday.
• Extreme hardship such as a family emergency, again with documentation.

Weddings and other special family events do not qualify as any of the above.  I cannot reschedule exams for purposes of more convenient travel, even if tickets have already been purchased.

Rescheduled exams and quizzes (those not arising from emergencies) must be taken prior to your (planned) absence.

If you require additional accommodations as determined by the Moses Center for Student Disabilities, please let us know as soon as possible.

New York University takes plagiarism and cheating very seriously and regards them as a form of fraud. Students are expected to conduct themselves according to the highest ethical standards. These offenses are all considered violations of academic integrity:

• Use of unauthorized resources for completion of assignments (e.g., a solution manual illegally purchased or downloaded or an internet community that provides answers);
• Nondisclosure of collaboration on homework or copying another student's written solution;
• Discussion of a quiz or exam between someone who has taken it and someone who has not;
• Copying another student's quiz or exam;
• Forging documentation to justify a makeup quiz or exam or late assignment.

There are of course other possibilities. Penalties range from a score of zero on a problem, assignment, quiz, or exam, to a failing grade in the course and notification of the student's Dean. Multiple violations can result in dismissal from the University.

## Schedule

Week Date Due Sections Contents
1 Jul 2 None (: 1.1 Systems of linear equations.
Jul 3 1.1: 1, 3, 7, 8, 11-14, 19, 22, 25 1.2 Row Reduction and Echelon Forms
Jul 4 Holiday (:
Jul 5 Quiz 1
1.2: 1, 3, 7-20, 23, 26
1.3
1.4
Vector Equations
The Matrix Equation Ax = b
2 Jul 9 1.3: 11-14, 17-22, 25, 26
1.4: 2, 4, 7, 9, 13, 15, 17, 19, 28, 30, 31
1.5
1.7
Solution Sets of Linear Systems
Linear Independence
Jul 10 1.5: 6, 10, 14, 22, 30, 32
1.7: 8, 11, 18, 26, 30, 40
1.8
1.9
Linear Transformations
The Matrix of a Linear Transformation
Jul 11 1.8: 6, 10, 12, 16, 24, 26, 28, 36
1.9: 6, 8, 10, 12, 14, 26, 28, 30, 32
2.1 Matrix Operations
Jul 12 Quiz 2
2.1: 10, 12, 13, 17-26
2.2
2.3
Inverse of a Matrix
Characterizations of Invertible Matrices
3 Jul 16 2.2: 6, 8, 12, 16, 17, 18 ,21 , 22, 32, 35
2.3: 6, 14, 15, 16, 21, 23, 24, 26, 36
3.1
3.2
Introduction to Determinants
Properties of Determinants
Jul 17 3.1: 4, 14, 16, 24, 32, 42
3.2: 8, 14, 20, 32, 34, 40
4.1 Vector Spaces and Subspaces
Jul 18 None (: 1.1-3.2 Review
Jul 19 None (: 1.1-3.2 Midterm
4 Jul 23 4.1: 2, 5-13, 16, 18, 19, 23, 24, 26, 32 4.2 Null Spaces, Column Spaces, and Linear Transformations
Jul 24 4.2: 4, 6, 8, 12, 18, 22, 24, 26, 28, 32 4.3
4.4
Linearly Independent Sets; Bases
Coordinate Systems
Jul 25 4.3: 8, 10, 12, 14, 20, 22, 24, 26
4.4: 4, 6, 10, 12, 22, 24, 28
4.5
4.6
Dimension of a Vector Space
Rank
Jul 26 Quiz 3
4.5: 10, 14, 18, 20, 22, 30
4.6: 4, 12, 16, 18, 22, 30
4.7 Change of Basis
5 Jul 30 4.7: 1-16 5.1
5.2
Eigenvectors and Eigenvalues
The characteristic Equation
Jul 31 5.1: 8, 14, 16, 18, 20, 22, 24, 27
5.2: 6, 12, 17, 18, 20, 21, 24
5.3 Diagonalization
Aug 1 5.3: 2, 4, 6, 10, 12, 14, 16, 18, 19, 20, 21, 22, 24, 26 5.4 Eigenvectors and Linear Transformations
Aug 2 Quiz 4
5.4: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 26
6.1 Inner Product, Length, and Orthogonality
6 Aug 6 6.1: 1-8, 12, 14, 16, 20, 24, 28, 30 6.2
6.3
Orthogonal Sets
Orthogonal Projections
Aug 7 6.2: 4, 8, 12, 14, 16, 20, 24, 26, 28
6.3: 8, 12, 14, 18, 20, 22
6.5 Least-Squares Problems
Aug 8 6.5: 6, 8, 12, 20 1.1-6.2 Review
Aug 9 None (: 1.1-6.2 Final