Linear Algebra 1

Lecturer:

Dana Majerová (gar.), Dana Majerová (gar.)

Tutor:

Dana Majerová (gar.), Dana Majerová (gar.)

Supervisor:

Synopsis:

Vector space R^n, linear independence, subspaces, base, dimension, coordinates. Linear mapping, kernel, rank, defect. Matrix, matrix of linear mapping. System of linear equations, Gaussian elimination.

Requirements:

Syllabus of lectures:

1. vector space R^n

2. linear dependence, linear independence

3. vektor subspaces

4. base and dimension

5. intersection and sum of subspaces

6. coordinates in given base

7. linear mapping

8. sum and multiple of linear mappings

9. matrix of mapping, matrix rank, regular matrix, inverse matrix

10. system of linear equations

11. Gaussian elimination, row operations

12. solution of system of linear equations

13. inverse matrix calcuation

Syllabus of tutorials:

1. vector space R^n

2. linear dependence, linear independence

3. vektor subspaces

4. base and dimension

5. intersection and sum of subspaces

6. coordinates in given base

7. linear mapping

8. sum and multiple of linear mappings

9. matrix of mapping, matrix rank, regular matrix, inverse matrix

10. system of linear equations

11. Gaussian elimination, row operations

12. solution of system of linear equations

13. inverse matrix calcuation

Study Objective:

Knowledge of basic terms of linear algebra.

Ability to prove mathematical theorems and solve problems of linear algebra, especially the system of linear equations.

Study materials:

Key references:

[1] Dontová, E. Matematika III. Praha: ČVUT, 1999.

[2] Čížková, L. Sbírka příkladů z matematiky I. Praha: ČVUT, 1999.

[3] Study materials and tasks in the MOODLE system (http://moodle.jadernaci.eu).

Recommended references:

[4] Pytlíček, J. Cvičení z algebry a geometrie. Praha: ČVUT, 1997.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: