# 2021/2022

## Content, progress and pedagogy of the module

### 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 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 eigenvalues and eigenvectors of matrices and their use
• Must have knowledge of projections and orthonormal bases

#### Skills

• Must be able to use computer software such as Matlab to solve linear algebra problems
• 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 matrix for a given linear transformation, and vice versa
• Must be able to solve simple matrix equations
• Must be able to compute determinants and could use the result of calculation
• Must be able to calculate eigenvalues and eigenvectors for simple matrices
• Must be able to determine whether a matrix is diagonalisable, and if so, implement a diagonalisation for simple matrices
• Must be able to compute the orthogonal projection onto a subspace of Rn
• Must be able to solve separable and linear first order differential equations, in general, and with initial conditions

#### 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

### Type of instruction

Oral or written examination. Exam format is decided on by start of semester.

## 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