(Created 2011-09-01.)

LINEAR ALGEBRA | FMA420 |

**Aim**

The course aims at giving a basic treatment of linear algebra. Particular emphasis is put on the role which this plays in applications in different areas of technology, in order to give the future engineer a good foundation for further studies in mathematics as well as other subjects. The aim is furthermore to develop the student's ability to solve problems and to assimilate mathematical text.

*Knowledge and understanding*

For a passing grade the student must

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 of its coupling to the concept of a linear transformation, and be able to carrry out elementary matrix operations and to solve matrix equations.

be able to give an overview of and illustrate mathematical concepts in linear algebra that are used to construct and study matematical models in the applications.

be able to explain the contents of some central definitions, theorems and proofs.

*Skills and abilities*

For a passing grade the student must

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. Rank. Linear transformations. Determinants. Eigenvalues and eigenvectors.

**Literature**

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