MA 322 001 Matrix Algebra and its Applications

Instructor: Rafael S. González D'León
Office: Patterson Office Tower, Room 767.
Office Hours: M 10:00AM to 11:00AM - W 11:00AM to 12:00PM or by appointment.

Course assistant: Robert Wolf
Office Hours: T 10:00AM to 11:00AM - R 9:30AM-10:30AM at The Mathskeller


Monday, Wednesday and Fridays 9:00AM-9:50AM CB 349.


Linear Algebra and its applications. David C. Lay. Fourth edition.

Course Contents

The solution of simultaneous linear equations. Matrix algebra. Determinants. Vector spaces. Eigenvalues and Eigenvectors. Inner product spaces and least squares approximation. Most of chapters 1 to 6 from Lay's book.

Examination and Grading

Tests (50%)

There will be 2 tests. These will be announced at least one week in advance.

Final (30%)

There will be a comprehensive final to be worth 30% on Wednesday 12/17/2014 8:00-10:00 A.M..

Homework and Quizzes (20%)

There will be both online homework and written homework to be handed in every week.
The online homework will be assigned and completed in Webwork ( Your username is your LinkBlue ID (use only capital letters), and your password is your student ID number (8 digits).
The written homework will be posted after every class in
The homework posted during each week will be due at the beginning of the class of Friday of the following week. Your written homework should:
  • Be clean and organized. Homework that cannot be understood to be graded will be awarded 0 points.
  • Be your own work. A reasonable amount of collaboration is expected but the written solutions should be your own and use your own words.
  • Show all your work. There will be no credit for correct answers if you do not show the steps you took to arrive to a solution. Partial credit will be awarded for your work even in the case you arrive to an incorrect answer.

There may also be some additional homework problems without any due date but that you should complete in order to train the concepts given in class. Some of these problems could appear in the quizzes, tests and the final. These problems will be assigned after some of the classes and also posted in the web page of the course.
There will be (unannounced) quizzes on some Wednesdays.
Homework and quizzes are equally weighted for the remaining 20% of the grade.

Grading Scale



This is an approximate schedule of the course containing the syllabus:
Wed 8/27Introduction. 1.1 Systems of Linear Equations
Fri 8/291.2 Row Reduction and Echelon Forms
Wed 9/31.3 Vector Equations
Fri 9/51.4 The Matrix Equation Ax = b
Mon 9/81.5 Solution Sets of Linear Systems
Wed 9/101.7 Linear Independence
Fri 9/121.8 Introduction to Linear Transformations
Mon 9/151.9 The Matrix of a Linear Transformation
Wed 9/172.1 Matrix Operations
Fri 9/192.2 The Inverse of a Matrix
Mon 9/222.3 Characterizations of Invertible Matrices
Wed 9/242.5 Matrix Factorizations
Fri 9/263.1 Introduction to Determinants
Mon 9/29Review Test 1
Wed 10/1TEST 1
Fri 10/33.2 Properties of Determinants
Mon 10/63.3 Cramer’s Rule, Volume, and Linear Transformations
Wed 10/84.1 Vector Spaces and Subspaces
Fri 10/104.1 Vector Spaces and Subspaces
Mon 10/134.2 Null Spaces, Column Spaces, and Linear Transformations
Wed 10/154.2 Null Spaces, Column Spaces, and Linear Transformations
Fri 10/174.3 Linearly Independent Sets; Bases
Mon 10/204.4 Coordinate Systems
Wed 10/224.5 The Dimension of a Vector Space
Fri 10/244.6 Rank
Mon 10/274.7 Change of Basis
Wed 10/294.9 Applications to Markov Chains
Fri 10/315.1 Eigenvectors and Eigenvalues
Mon 11/35.2 The Characteristic Equation
Wed 11/55.3 Diagonalization
Fri 11/75.4 Eigenvectors and Linear Transformations
Mon 11/10Review Test 2
Wed 11/12TEST 2
Fri 11/145.5 Complex Eigenvalues
Mon 11/1710.2 The Steady-State Vector and Google's PageRank
Wed 11/19More applications of Eigenvalues and Eigenvectors
Fri 11/216.1 Inner Product, Length, and Orthogonality
Mon 11/246.1 Inner Product, Length, and Orthogonality
Mon 12/16.2 Orthogonal Sets
Wed 12/36.3 Orthogonal Projections
Fri 12/56.4 The Gram—Schmidt Process
Mon 12/86.5 Least-Squares Problems
Wed 12/106.8 Applications of Inner Product Spaces
Fri 12/12Review Final
Wed 12/17FINAL EXAM 8:00-10:00 A.M.

Additional Resources

The university and the department of mathematics offer tutoring without appointment at The Mathskeller . The Study also offers peer tutoring.

Calculators Policy

Calculators are not allowed in quizzes, tests or the final exam.

Code of Conduct

Students should consult the students rights and responsibilities outlined in the Student Code of Conduct. Any offense to the Code of Conduct will result in a grade of "E" for the course and a referral to the Dean of Students.

Students with Disabilities

Students with documented physical‚ learning‚ or temporary disabilities may receive assistance and support from the Disability Resource Center. It is recommended that students contact the Disability Resource Center early to request specific assistance so that the required medical or psychological documentation can be reviewed and reasonable accommodations can be provided from the beginning of class work in order to achieve the greatest benefit to the student.

Changes to this Syllabus

This syllabus can have some changes during the semester. It is responsibility of the students to visit frequently the webpage of the course for up to date information.