(Created 2011-09-01.)

MATHEMATICS, LINEAR ALGEBRA | FMA656 |

**Aim**

The course aims at giving a basic treatment of linear algebra. Particular emphasis is given to the role which the latter plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies.

*Knowledge and understanding*

For a passing grade the student must

- with confidence be able to solve linear systems of equations and be able to demonstrate an ability to geometrically interpret such systems
- be able to represent, handle and compute with basic geometrical objects in three dimensions, such as points, vectors, lines and planes
- be able to show a general knowledge of the matrix concept, and be able to carrry out elementary matrix operations and to solve matrix equations.

*Skills and abilities*

For a passing grade the student must

- be able to demonstrate a good capacity for algebraic manipulations.
- in connection with problem solving be able to demonstrate an ability to independently choose and use mathematical methods within linear algebra
- in connection with problem solving be able to demonstrate an ability to integrate concepts from different parts of the course
- be able to demonstrate an ability to explain mathematical reasoning in a structured and logically clear way.

**Contents**

Systems of linear equations. Vectors. Bases and coordinate systems. Equations for lines and planes in space. Scalar product with applications. Vector product with applications. Matrices. Linear transformations. Determinants.

**Literature**

Sparr, G: Linjär algebra. Studentlitteraturm 1997. ISBN: 9789144197524.