Linear Algebra
LA-3-BP
| Subject | Linear Algebra (LA) |
| Guarantee |
Mgr. Vojtěch Růžička, Ph.D. |
| Department | Department of Mathematics and Physics |
| Specialization | NO |
| Profiling subject | YES |
| Theory profiling subject | NO |
| Final exam | NO |
| Multi semestral subject | NO |
| Subject is guaranted by other school | NO |
| Optionality | Povinný |
| Clasification | Klasifikovaný zápočet |
| Credits | 3 |
| Recommended year/semester | 1/1 |
| Number of weeks | 14 |
| Celkem (h) | Př. | Cv. | Lab. | Sem. | Kurzy | Praxe | Stáže | Soustř. | Exkurze | Terén | SP | Konzultace | PV | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Matrices: – definition, types of matrices, – operations on matrices, transposition, – elementary operations on matrices, – linear independence of rows and columns, (row/column) rank, inverse matrix. | 8 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Determinants: – definition and properties, Sarrus rule, – Laplace cofactor expansion theorem, – evaluation of inverse matrix using matrix of cofactors. | 8 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Systems of linear algebraic equations: – matrix notation, solvability, homogeneous systems, – Gaussian elimination method and Jordan method, – solution using inverse matrix, Cramer's rule, eigenvalues and eigenvectors of matrices. | 8 | 4 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Vectors in the plane and space: – free and fixed vectors, linear independence, basis and coordinates, – scalar, vector and mixed products, – lines and planes in the space. | 4 | 2 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Povinná:
Kropáč, J., Vetchý, V. Matice, determinanty, soustavy rovnic. Skriptum. 3. vydání. Brno: Vojenská akademie v Brně, 1999. ii+51 s. Dostupné v knihovně UO pod číslem S-2581/A.
Kuben, J., Račková, P. Vektory a analytická geometrie. Skriptum. Brno: Univerzita obrany, 2014. 33 s. Dostupné z https://moodle.unob.cz/mod/resource/view.php?id=51662 [cit. 2020-07-25].
Kropáč, J., Vetchý, V. Matice, determinanty, soustavy rovnic. Skriptum. 3. vydání. Brno: Vojenská akademie v Brně, 1999. ii+51 s. Dostupné v knihovně UO pod číslem S-2581/A.
Kuben, J., Račková, P. Vektory a analytická geometrie. Skriptum. Brno: Univerzita obrany, 2014. 33 s. Dostupné z https://moodle.unob.cz/mod/resource/view.php?id=51662 [cit. 2020-07-25].
Písemné testy během semestru, stanovené úkoly, klasifikovaný zápočet.