# 2022/2023

## Content, progress and pedagogy of the module

Linear algebra is a fundamental tool for virtually all engineering mathematics.

### Learning objectives

#### Knowledge

• Must have knowledge about definitions, results and techniques within the theory of systems of linear equations
• Must be able to demonstrate insight into linear transformations and their connection with matrices
• Must have obtained knowledge about the computer tool MATLAB and how it can be used to solve various problems in linear algebra
• Must have acquired knowledge of simple matrix operations
• Must know about invertible matrices and invertible linear mappings
• Must have knowledge of the vector space Rn and various subspaces
• Must have knowledge of linear dependence and independence of vectors and the dimension and bases of subspace
• Must have knowledge of the determinant of matrices
• Must have knowledge of Eigen values and eigenvectors of matrices and their use
• Must have knowledge of projections and orthonormal bases
• Must have knowledge of first order differential equations, and on systems of linear differential equations

#### Skills

• Must be able to apply theory and calculation techniques for systems of linear equations to determine solvability and to provide complete solutions and their structure
• Must be able to represent systems of linear equations using matrix equations, and vice versa
• Must be able to determine and apply the reduced Echelon form of a matrix
• Must be able to use elementary matrices for Gaussian elimination and inversion of matrices
• Must be able to determine linear dependence or linear independence of small sets of vectors
• Must be able to determine the dimension of and basis for small subspaces

#### Competences

• Must demonstrate development of his/her knowledge of, understanding of, and ability to make use of, mathematical theories and methods within relevant technical fields
• Given certain pre-conditions, must be able to make mathematical deductions and arguments based on concepts from linear algebra

### Type of instruction

Refer to the overview of instruction types listed in § 17. The types of instruction for this course are decided according to the current Joint Programme Regulations and directions are decided and given by The Study Board of Electronics and IT.

## 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