# 2020/2021

## Prerequisite/Recommended prerequisite for participation in the module

A-level mathematics from a Danish high school or equivalent.

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

Students who have passed the module should be able to explain

• 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
• Digitalized self-study
• Workshops on calculus problems relevant to the study programme.

150 hours

## 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