Linear Algebra I

Office hours: by appointment. I will be in Friday 6 January 10:30 - 12:30, in S125 (Malostranské nám. 25, 1st floor).

Exercises

Lectures for the course Linear Algebra I in the winter semester of 2016 are given by Jiri Fiala.

Course syllabus. Exam topics list (JF)

The online collection of exercises provides further practice problems supplementary to those given in class.

Sage may be helpful in tackling some of the exercises (just a few basic commands are needed to perform the calculations needed for this course - you will be able to register for a Sage account at the beginning of the semester).

Weekly exercises will be given as homework. These are not formally graded, but students may be asked to present solutions in the tutorial class the week after receiving the exercise sheet. Short tests on routine aspects of the course will occasionally be given in class to check that all is going well. Performance on homework exercises will not directly affect your grade for the main course. However, if you intend to be graded for the main course, you require a "pass" for the exercises. A pass/fail grade for the exercises will be decided based on regular attendence and participation in class, and satisfactory performance on the short tests during the semester and the longer test at the end.

Exercise classes are held at 14:00 on Tuesdays in semester (except for Dean's Day on 8.11.2016) in Room S6 in the MFF building in Mala Strana (lectures are in the same room at 9:00 on Wednesdays).

Resources

Robert Beezer, A First Course in Linear Algebra - a free online textbook.

MIT's website includes video lectures and supplementary material to Gilbert Strang's Introduction to Linear Algebra. Strang's own sample material etc.

Jiri Matousek's preliminary version of the recommended book Thirty-three miniatures: mathematical and algorithmic applications of linear algebra.

M. Anderson and T. Feil, A First Course in Abstract Algebra: Rings, Groups, and Fields, CRC, 2015 (chapters 17-19 for groups).

F. Goodman, Algebra: Abstract and Concrete, edition 2.6

Permutations (Cut-the-Knot.org)

Exercise sheets

Answers to some excercises may take the form of Sage worksheets posted online. Handwritten work on exercises please hand in at the beginning of the following class for marking.

4 October

11 October (Questions 1 and 2 for handing in 17 October; Question 3 collaboratively. In addition, if you do not know Sage, please be sure to register for a Sage account, and as a warm-up work through the worksheet entitled "Sage GS: Getting Started" which is at the bottom of this page of the section on Solving Systems of Linear Equations in the online book A First Course in Linear Algebra)

Elementary row operations: supplement to exercise class - includes proofs that elementary row operations preserve solution sets of systems of linear equations.

18 October

Sage account. Gaussian Elimination Sage worksheet

Rank uniqueness numerical example (JF)

Computer package problem (for practicing using Sage - guess pattern, check with calculation for larger matrices)

25 October. No class due to Matriculation Day.

1 November.

Solutions to Exercise Sheet 3 (Sage worksheet)

(Partial) solution to computer package problem (Sage worksheet).

Matrix properties exercise

8 November. No class (Dean's Day).

Solution to problem 2 on exercise sheet 4 (Gauss elimination for matrix with variable entries).

15 November.

K. Conrad, The 15-puzzle (and Rubik's cube)

22 November. (In question 4, there was a missing cardinality sign around I(p) in the exponent of (-1) which has now been corrected.)

29 November.

Solutions

6 December.

Solutions

13 December.

Solutions

20 December.

Solutions

10 January

TEST on basic definitions and examples on the following topics: Elementary row operations, Row echelon form, Systems of linear equations, Matrices, Groups, Permutations, Fields, Matrices over finite fields, Vector spaces, Linear independence, Bases.