# Linear Algebra and Geometry I

5 credits

Syllabus, Bachelor's level, 1MA025

Code
1MA025
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 26 October 2021
Responsible department
Department of Mathematics

## Entry requirements

Participation in Basic Course in Mathematics or Introduction to Studies in Mathematics, which also may be taken in parallel with this course.

## Learning outcomes

On completion of the course the student should be able to

• solve systems of linear equations using Gaussian elimination and be able to explain the relation between solvability and rank;
• use matrix algebra, in particular know how to compute the inverse of a matrix, and know how to compute determinants, and be able to interpret m×n matrices as linear transformations from Rn to Rm;
• explain the basic properties of two- and three-dimensional vectors, master elementary vector algebra, decide if vectors are linearly independent, and be familiar with the concepts of basis and coordinates;
• give an account of the concepts of scalar product and vector product, know how to compute such products and how to interpret them geometrically;
• determine the equations for a line and a plane and how to use these for computing intersections and distances;
• define rotations, reflexions and orthogonal projections in two and three dimensions and be able to compute their matrices;
• formulate important results and theorems covered by the course;
• use the theory, methods and techniques of the course to solve mathematical problems;
• present mathematical arguments to others.

## Content

Linear systems of equations: Gaussian elimination, rank, solvability. Matrices: matrix algebra and matrix inverse. Determinants. Vector algebra, linear dependence and independence, bases, coordinates, scalar product and vector product, equations for lines and planes, distance, area and volume. Description of rotations, reflections and orthogonal projections in R2 and R3. The linear space Rn and m×n matrices as linear transformations from Rn to Rm. The standard scalar product on Rn and the Cauchy-Schwarz inequality.

## Instruction

Lectures, problem solving sessions and team-working.

## Assessment

Written examination at the end of the course (4 credits) and assignments (1 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

## Other directives

The course cannot be included in higher education qualification together with the course Algebra and vector geometry.