# 2019/2020

## Prerequisite/Recommended prerequisite for participation in the module

The module builds on knowledged from the module Calculus.

## Content, progress and pedagogy of the module

### Learning objectives

#### Knowledge

• Have knowledge about definitions, results and techniques in the theory of systems of linear equations
• Be able to demonstrate insight into linear transformations and their connection to matrices
• Have obtained knowledge about the computer program MATLAB, and its application related to linear algebra
• Have acquired knowledge about simple matrix operations
• Have knowledge about invertible matrices and invertible linear transformation
• Have knowledge about the vector space Rn and its subspaces
• Have knowledge about linearly dependent vectors and linearly independent vectors, and the dimension and basis of subspaces
• Have knowledge about the determinant of a matrix
• Have knowledge about eigenvalues and eigenvectors of matrices and their application
• Have knowledge about projections and orthonormal bases
• Have knowledge about first-order differential equations, and systems of linear differential equations

#### Skills

• Be able to apply theory and calculation techniques for systems of linear equations to determine solvability and determine complete solutions and their structure
• Be able to represent systems of linear equations by means of matrix equations, and vice versa
• Be able to determine and apply the reduced echelon form of a matrix
• Be able to use elementary matrices in connection with Gauss elimination and inversion of matrices
• Be able to determine linear dependence or linear independence of sets of few vectors
• Be able to determine dimension of and basis of subspaces
• Be able to determine the matrix for a given linear transformation, and vice versa
• Be able to solve simple matrix equations
• Be able to calculate the inverse of small matrices
• Be able to determine the dimension of and basis for kernel and column spaces
• Be able to calculate determinants and apply the result of this calculation
• Be able to calculate eigenvalues and eigenvectors for simple matrices
• Be able to determine whether a matrix is diagonalizable, and if so, be able to diagonalize a simple matrix
• Be able to calculate the orthogonal projection onto a subspace of Rn
• Be able to solve separable and linear first order differential equations, in general, and with initial conditions

#### Competences

• Be able to develop and strengthen knowledge, comprehension and application of mathematical theories and methods in other subject areas
• Given certain pre-conditions, be able to make mathematical deductions and arguments based on concepts from linear algebra

### Type of instruction

Lectures with exercises.

### Extent and expected workload

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

## Facts about the module

 Danish title Lineær algebra Module code F-MAT-B2-2 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 Morten Grud Rasmussen

## Organisation

 Study Board Study Board of Mathematics, Physics and Nanotechnology Department Department of Mathematical Sciences Faculty Faculty of Engineering and Science