# MATP121 Linear Algebra and Geometry 1 (7 cr)

Study level:
Basic studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024

## Description

Linear algebra and geometry of euclidean spaces. Main themes: Systems of linear equations, linear independence, subspaces, basis, dimension, orthogonality, matrices, determinants.

The contents correspond to

Lay: Linear algebra and its applications, 2nd edition chapters 1-4 and 6

## Learning outcomes

After completing the course, the student- is able to solve multivariate linear equations using the the method of Gauss and Jordan, and to analyze the solutions sets.

• knows the linear structure of Euclidean space, especially subspaces, as well as inner product and norm
• is able to handle linear mappings, matrices and determinants, and knows the relationships between them
• is able to determine whether a given set of vectors is linearly independent
• can form a base for a given subspace and determine the dimension of the subspace
• knows how to use the geometric structure provided by Euclidean inner product, is able to form an orthonormal base for a given subspace using the Gram and Schmidt orthogonalization method, and knows how to compute the orthogonal projection to a subspace
• knows the definitions of the key concepts of linear algebra and is able to produce proofs

## Description of prerequisites

Good command of the long mathematics curriculum of high school.

## Literature

• Steven J. Leon, Linear Algebra with Applications, Pearson Education, Inc. (kaikki painokset käyvät); ISBN: 0-13-200306-6
• Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambrige Press. (kaikki painokset käyvät); ISBN: 978-09802327-7-6
• Stanley I. Grossman, Elementary Linear Algebra, Wadswoth Publishing Company. (kaikki painokset käyvät).; ISBN: 0-534-07422-7
• Roland E. Larson ja Bruce H. Edwards, Elementary Linear Algebra, D.C. Heath and Company. (kaikki painokset käyvät); ISBN: 0-669-14583-1
• David C. Lay, Linear Algebra and Its Applications, Pearson Education, Inc. (kaikki painokset käyvät); ISBN: 0-321-14992-0

## Completion methods

### Method 1

Description:
Suoritustavassa opintojakso suoritetaan välikokeilla (2kpl kurssin aikana). Suoritustapaan liittyy viikottaisten harjoitustehtävien tekemistä. Osa harjoitustehtävistä voi olla kirjallisesti palautettavia. Välikokeisiin saa lisäpisteitä tehdyistä harjoitustehtävistä. Tarkemmat tiedot opetusohjelmassa.
Evaluation criteria:
Grading is based on points from mid exams and weekly exercises
Time of teaching:
Period 1, Period 2
Select all marked parts

### Method 2

Description:
Suoritustapana itsenäinen opiskelu ja lopputentti.
Evaluation criteria:
Grading is based on points from the final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (7 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Opintojakson arvosana määräytyy välikokeiden yhteispistemäärän ja laskuharjoitustehtävistä saatavien pisteiden perusteella.
Language:
Finnish
Study methods:

Lectures 48 h (in Finnish), exercises

Study materials:

Luennoilla jaettava luentomateriaali.

x

Type:
Exam