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.
