University of West Bohemia
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for academic year 2024/2025
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Course: Linear Algebra

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Course title Linear Algebra
Course code KMT/LA
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Winter
Number of ECTS credits 5
Language of instruction Czech, English
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Honzík Lukáš, PhDr. Ph.D.
  • Königsmarková Soňa, Mgr. et Mgr. Ph.D.
Course content
1. Vector space, axioms and basic properties 2. Vector subspace, span of a set of vectors, spanning set for a vector subspace 3. Linear dependence and independence of a family of vectors 4. Basis of a vector space, coordinates of a vector with respect to the given basis 5. Dimension of vector space, sum of subspaces, theorem on the dimension of a sum 6. Matrix algebra 7. Rank of matrix, Gaussian elimination method 8. Solving systems of linear equations using matrices, Frobenius's theorem 9. Linear maps (homomorphims) of vector spaces, coordinate matrix representations 10. Euclidean vector space, inner product, vector norm, angles between vectors 11. Ortogonal and ortonormal basis of space, Gram-Schmidt process of ortonormalization 12. Determinant of matrix, definition and basic properties, methods of computation 13. Cramer's rule, its application for solving systems of linear equations

Learning activities and teaching methods
Interactive lecture, Lecture with practical applications, Collaborative instruction, Lecture, Practicum
  • Preparation for an examination (30-60) - 45 hours per semester
  • Preparation for formative assessments (2-20) - 15 hours per semester
  • Contact hours - 52 hours per semester
prerequisite
Knowledge
have the knowledge specified in the "Catalog of requirements for the matriculation examination in mathematics" valid for the current school year
Skills
apply the knowledge and skills described in the "Catalog of requirements for the matriculation examination in mathematics" valid for the current school year
Competences
N/A
N/A
N/A
learning outcomes
Knowledge
decide whether the set of vectors forms the basis of vector space
apply the Gaussian elimination algorithm
give examples of defined concepts and their properties described in mathematical theorems
Skills
prove the validity of simple statements in vector space
decide on the linear dependence or independence of a set of vectors
solve a system of m linear equations of n unknowns over a commutative field
calculate a determinant
Competences
N/A
teaching methods
Knowledge
Lecture
Interactive lecture
Practicum
One-to-One tutorial
Skills
Lecture
Practicum
Skills demonstration
One-to-One tutorial
Competences
Lecture
Lecture supplemented with a discussion
Practicum
Self-study of literature
One-to-One tutorial
assessment methods
Knowledge
Combined exam
Test
Continuous assessment
Oral exam
Skills
Combined exam
Test
Skills demonstration during practicum
Continuous assessment
Competences
Combined exam
Recommended literature
  • Bečvář, Jindřich. Lineární algebra. Praha, 2002. ISBN 80-85863-92-8.


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): Information Technologies in Education (18) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (19) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (19) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (18) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): English Language in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): English Language in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (15) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (19) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Russian Language in Education (19) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (17) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (19) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Russian Language in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): History in Education (17) Category: History courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (14) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (19) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (18) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (19) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Music in Education (19) Category: Art and applied art 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (16) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (16) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (18) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Technology and Design in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Russian Language in Education (18) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): History in Education (18) Category: History courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (17) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (16) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (16) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (1) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (17) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (16) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Chemistry in Education (18) Category: Chemistry courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (18) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Biology in Education (17) Category: Biology courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): English Language in Education (17) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physical Education in Education (19) Category: Physical education and sport 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Information Technologies in Education (15) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (15) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Studies in Mathematics (17) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (17) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Physics in Education (16) Category: Physics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Education Study plan (Version): Geography in Education (15) Category: Pedagogy, teacher training and social care 1 Recommended year of study:1, Recommended semester: Winter
University of West Bohemia, date of update: 26.07.2024 23:53. Data created for academic year 2024/2025