# 2020/2021

## Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledge from the module Calculus.

## 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
• The connection between a vector space of dimension n and Rn
• Orthogonality and orthonormal bases

#### 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.
• Given a basis for a vector space finding coordinates for vectors and the matrix of a linear map.
• Gram Schmidt, projection on a subspace, projection matrices. Coordinates for a vector wrt. an orthonormal basis.

#### Competences

Can apply methods and concepts from linear algebra, including vector spaces and orthonormal bases 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 137,5 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