# 2022/2023

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

• Vectors, matrices and systems of linear equations
• Connections between solution of systems of linear equations, associated matrices and operations on those
• Linear independence and dimension.
• Eigenvalues and eigenvectors
• The connection between properties of a matrix and of the echelon form of it
• Linear programming: Possibilities and limitations
• The least square method and the connetion to orthogonal projection. Orthogonal and symmetric matrices.

#### Skills

• Matrix-vector product, product and sum of matrices. Row operations. Gauss elimination.
• Eigenvalues and eigenspaces.
• Solution of a system of linear equations on vector form.
• Bases of subspaces associated with a matrice.
• The simplex method. Converting to standard form.
• The least square method on a data set.

#### Competences

Can apply methods and concepts from linear algebra, including linear programming and orthogonal projections to given problems relevant to the study programme.

### Type of instruction

Lectures, exercises, videos, quiz, digitalised self-study, workshops on calculus problems relevant to the study programme.

Since it is a 5 ECTS course, the work load is expected to be 150 hours for the student.

## Exam

### Exams

 Name of exam Linear Algebra Type of exam Written or oral exam ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment The criteria of assessment are stated in the Examination Policies and Procedures

 Danish title Lineær algebra Module code MAT2LIAL1257 Module type Course Duration 1 semester Semester Spring ECTS 5 Language of instruction Danish and English Empty-place Scheme Yes Location of the lecture Campus Aalborg, Campus Esbjerg Responsible for the module Lisbeth Fajstrup

## Organisation

 Study Board Study Board of Mathematical Sciences Department Department of Mathematical Sciences Faculty Faculty of Engineering and Science