Linear Algebra

2022/2023

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 examLinear Algebra
Type of exam
Written or oral exam
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleLineær algebra
Module codeF-MAT-B2-2
Module typeCourse
Duration1 semester
SemesterSpring
ECTS5
Language of instructionDanish and English
Empty-place SchemeYes
Location of the lectureCampus Aalborg, Campus Esbjerg
Responsible for the module

Organisation

Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyFaculty of Engineering and Science