Introduction to Linear Algebra

Course code

MLM6182.DT

old course code

Course title in Estonian

Lineaaralgebra algkursus

Course title in English

Introduction to Linear Algebra

ECTS credits

4.0

approximate amount of contact lessons

32

Teaching semester

spring

Assessment form

Examination

lecturer of 2020/2021 Autumn semester

õppejõud on määramata

lecturer of 2020/2021 Spring semester

lecturer not assigned

Course aims

The aim of the course is to provide an overview of the concepts of matrix, linear space, system of linear equations and complex numbers.

Brief description of the course

1.Complex numbers and operations with complex numbers. Different forms of complex numbers.

2.Matrices and operations with matrices.

3.Permutations and inversions. Determinants and their properties. Minors. Laplace expansion.

4.Determinant of the product of matrices. Inverse of a matrix, it’s calculation methods and properties.

5.Linear space. Linear independence of the set of vectors. Basis of the linear space.

6.Systems of linear equations: homogeneous system of lineaar equations and nonhomogeneous system of linear equations. Gaussian elimination method.

7.Systems of linear equations: Cramer’s rule.

2.Matrices and operations with matrices.

3.Permutations and inversions. Determinants and their properties. Minors. Laplace expansion.

4.Determinant of the product of matrices. Inverse of a matrix, it’s calculation methods and properties.

5.Linear space. Linear independence of the set of vectors. Basis of the linear space.

6.Systems of linear equations: homogeneous system of lineaar equations and nonhomogeneous system of linear equations. Gaussian elimination method.

7.Systems of linear equations: Cramer’s rule.

Independent work

Home assignments

Learning outcomes in the course

After passing this course, the student:

Knows matrices, linear spaces, systems of linear equations and complex numbers.

Is able to solve the standard exercises about the systems of linear equations, matrices and complex numbers.

Knows matrices, linear spaces, systems of linear equations and complex numbers.

Is able to solve the standard exercises about the systems of linear equations, matrices and complex numbers.

Assessment methods

Homework and class-tests. The exam contains two theoretical questions and one practical one.

Teacher

dots Alar Leibak

Replacement literature

Kangro, G. Kõrgem algebra. Tallinn: 1962;

Kilp, M. 2005 Algebra I. Tartu: TÜ.

Lõhmus, A.; Petersen, I.; Roos, H. 1982 Kõrgema matemaatika ülesannete kogu;

Paal, E. 2000 Lineaaralgebra elemente. TTÜ, Tallinn.

Kilp, M. 2005 Algebra I. Tartu: TÜ.

Lõhmus, A.; Petersen, I.; Roos, H. 1982 Kõrgema matemaatika ülesannete kogu;

Paal, E. 2000 Lineaaralgebra elemente. TTÜ, Tallinn.