## 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:
MB003/01: Fri 14:00–15:50 G123, 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
Literature
• Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
• Zlatoš, Pavol. Lineárna algebra a geometria. Předběžná verze učebních skript MFF UK v Bratislavě.
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