Course: Linear algebra

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Course title Linear algebra
Course code KMA/LA
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Pech Pavel, prof. RNDr. CSc.
  • Hašek Roman, Mgr. Ph.D.
Course content
1. Matrices. 2. Algebraic operations with matrices. 3. Multiplication of matrices. 4. Gaussian elimination. Rank of a matrix. 5. Inverse matrix. Computation using the Gaussian elimination. 6. Permutations. 7. Determinant. Singular and regular matrix. 8. Computation of the determinant using the minor expansion. 9. Applications of determinants. 10. Inverse matrix. Computation using the adjoint matrix. 11. Solving of regular systems of linear equations. Cramer's rule. Use of the inverse matrix. 12. Systems of linear equations. Frobenius theorem. 13. Homogeneous and nonhomogeneous systems of linear equations. 14. Applications.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
  • Preparation for exam - 28 hours per semester
Learning outcomes
Matrix and its properties, permutations, determinants, system of linear equations, Frobenius theorem.
A graduate will understand basic terms from Linear algebra and their applications within the range of the curriculum of the subject. She will learn corresponding computational skills, especially operations with matrices, determinants and solving of systems of linear equations.
Prerequisites
no prerequisites

Assessment methods and criteria
Combined exam

Active participation on seminars, written and oral examination
Recommended literature
  • Bican, L.:. Lineární algebra. Praha, SNTL, 1979.. Praha, SNTL, 1979.
  • Krieg, J., Vaňatová, L.:. Analytická geometrie lineárních útvarů. České Budějovice, PF JU, 1994..
  • Skalská, D.:. Algebra, Olomouc, 2006..
  • Tlustý, P.:. Lineární algebra pro učitele. České Budějovice, PF JU, 2003.. České Budějovice, PF JU, 1994.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Introductory teacher training course in mathematics (3) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter