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FI:MB003 Linear Algebra and Geometry I - Course Information

## MB003 Linear Algebra and Geometry I

**Faculty of Informatics**

Spring 2012

**Extent and Intensity**- 2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
**Teacher(s)**- doc. RNDr. Jan Paseka, CSc. (lecturer)

Mgr. Jiří Janda, Ph.D. (seminar tutor)

Mgr. Radek Šlesinger, Ph.D. (seminar tutor) **Guaranteed by**- doc. RNDr. Jan Paseka, CSc.

Faculty of Informatics

Supplier department: Faculty of Science **Timetable**- Fri 12:00–13:50 G123
- Timetable of Seminar Groups:

*J. Paseka*

MB003/02: Mon 10:00–11:50 G125,*J. Janda* **Prerequisites**(in Czech)- !
**MB102**Mathematics II &&! NOW (**MB102**Mathematics II ) **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- there are 13 fields of study the course is directly associated with, display
**Course objectives**- Linear algebra belongs to the fundamentals of mathematical education. Passing the course, the students should - master the basic notions concerning vector spaces and linear maps and, furthermore, they should - gain good computational skills with matrices and systems of linear equations.
**Syllabus**- Scalars, vectors and matrices: Properties of real and
complex numbers, vector spaces and their examples,
$
**R**^n$ and $**C**^n$, multiplication of matrices, systems of linear eguations, Gauss elimination, computation of inverse matrices. - Vector spaces - basic notions: Linear combinations, linear independence, basis, dimension, vector subspaces, intersections and sums of subspaces, coordinates.
- Linear mappings: Definition, kernel and image, linear isomorphism, matrix of linear mapping in given bases, transformation of coordinates.
- Systems of linear equations: Properties of sets of solutions, rank a matrix, existence of solutions.
- Determinants: Permutations, definition and basic properties of determinants, computation of inverse matrices, application to systems of linear equations.
- Affine subspaces in $
**R**^n$: Definition, parametric and implicit description, affine mapping. - Scalar product in $
**R**^n$: Definition and basic properties of scalar product

- Scalars, vectors and matrices: Properties of real and
complex numbers, vector spaces and their examples,
$
**Literature**- Slovák, Jan.
*Lineární algebra*. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné nahttp://www.math.muni.cz/~slovak . - Zlatoš, Pavol. Lineárna algebra a geometria. Předběžná verze učebních skript MFF UK v Bratislavě.

- Slovák, Jan.
**Teaching methods**- Lectures: theoretical explanation with practical examples. Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Students will be asked to have an active participation at seminars and to obtain 40 % of possible points from two written tests.
**Assessment methods**- Form: lectures and exercises. Exam: written. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
**Language of instruction**- Czech
**Follow-Up Courses****Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses****Teacher's information**- http://www.math.muni.cz/~cadek

- Enrolment Statistics (recent)

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