Math 4242
Spring 2016

Home Syllabus Preview Questions
Homework Exams Useful hints



  • (4/28) Hw12 is posted.
  • (4/22) Hw11 is updated and preview question 10, homework solutions 9 and 10 are posted.
  • (4/20) Hw 11 and the solution for p9 are posted.
  • (4/16) Preview question 9 posted.
  • (4/12) Hw10, grade distribution for midterm 2 are posted.
  • (4/9) Preview question 8 posted.
  • (4/5) Practice exam 2 solution is corrected (prob. 2 -1/3->1/3 and -1/5-> 1/5). Homework solution 7 and 8 are posted.
  • (4/4) Practice exams and solutions are posted.
  • (3/31) Hw 9 is updated.

Course Description,  Prerequisites and Other Courses

Prerequisite: Math 2243 (Linear Algebra and Differential Equations) or 2373 or 2573 (as suggested by the School of Mathematics).

The following knowledge is assumed: systems of linear equations, Gaussian elimination, determinants, vector spaces, linear independence, basis and dimension. However I will review these briefly.

New topics include the Cramer's rule, the row, column spaces, linear transformations, inner product, orthogonality, the Gram-Schmidt algorithm, eigenvalues and eigenvectors, diagonalization, hermitian matrices, the singular value decomposition, quadratic forms, positive definite matrices, the Jordan canonical forms and some applications of these topics. The lectures follow the text fairly closely except those applications.

For a detailed syllabus see the Syllabus page.


  • Applied Linear Algebra, by Peter J. Olver and Chehrzad Shakiban - Book webpage (including errata). This course basically covers Chapters 1, 2, 3, 5, 7 and 8 of the textbook and some applications of linear algebra.

Instructor and Office Hours

  • Instructor: Yu-jong Tzeng, Vincent Hall 451

  • Email: ytzeng "at" 

  • Office Hours: Monday 6:10-8:00pm, Wednesday 3:30-5pm,  and by appointment. Also feel free to ask questions by email.

Time and location

Lec 003: 12:20 PM - 01:10 PM @ Vincent Hall 211

Lec 005: 02:30 PM - 03:20 PM @ Vincent Hall 211


Grades will be based on the following percentages. The class will be graded relative to a curve, curved by the total final score. The curve, however, has no “average” set in advance: a strong performance by many students will earn a high average for the class and vice-versa.

The grades will be recorded on moodle. Please check your scores frequently and report to Yu-jong ASAP if there's any error.

Preview Questions

Preview questions are designed to give you motivations to preview the material for the next week on weekends. They are due on every Monday, starting at 1/24 but the first one is only for practice and will not be counted. Every week a link will be posted here. You need to login using your university ID and everyone can only submit one answer but the answer can be modified before the deadline. The lowest two scores will be dropped.

There will be 5 short questions each week, and you get 4 points for a correct answer, 3 points for an incorrect answer and 0 points for leaving it blank.


There will be weekly homework assignments. Homework should be turned in class or to Yu-jong's mailbox on the first floor of Vincent Hall. Homework is due by 4:30 pm on Wednesdays. Late homework will not be accepted. The lowest 2 homework grades will be dropped.

Please write legibly, never forget to put your name and your section number on the top of your work. Although you are encouraged to discuss homework problems with your classmates, you have to turn in your own work based on your own understanding. Read the assignments carefully. You do not get partial credits for doing wrong problems. Please see homework policy for more information.

You should solve the homework questions in order; multiple sheets should be stapled together. Answers should be simplified when possible and kept in exact form (i.e., do not give a decimal approximation unless specifically asked).


There will be weekly 5-min quizzes in the beginning of Friday classes. These problems will be similar to homework problems. It will be designed based mainly on material from the previous week and might be related to material before.

The lowest 2 quiz grades will be dropped to accommodate an absence, bad day, etc... However, if you need to miss multiple quizzes due to a religious observance, family emergency or academic reason, let me know in advance.


There will be two midterm exams and a final exam.

The problems on the exams will be similar to examples done in class and homework problems. Please check exam policy.

No calculators, notes and books are allowed for any of the exams.

Additional Help

  • MIT's Linear Algebra Homepage: (with a variety of resources, including the videos of Prof. Gil Strang's lectures at MIT)

  • (as a reference, MIT's book) by Professor Gilbert Strang ( at MIT, Introduction to Linear Algebra (4th Ed., 2009), Wellesley-Cambridge Press.

Useful Links

  • Disability Accommodation: If you have, or think you may have, a disability (e.g., mental health, attentional, learning, chronic health, sensory, or physical), please contact the Disability Resource Center at 612-626-1333 to arrange a confidential discussion regarding equitable access and reasonable accommodations.  Please also discuss with Yu-jong early in the semester to review how the accommodations will be applied in the course (at least one week before the first midterm).

  • Matlab is a powerful math software to do computations of matrices. You can get a student license here. Prof. Rick Moeckel's guide1 and guide 2 to use basic commands.

  • University Policy Statements: The University Senate statements regarding academic dishonesty, credit, and workload expectations, and grading standards are at: and

Last updated: April 12, 2016.
Spring 2016 -- Department of Mathematics, University of Minnesota
Problems with this page? Contact ytzeng "at" so we can fix the problem.