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