In this course, the most important subjects regarding linear algebra of a finite number of variables are treated. The purpose is to make the students acquainted with techniques in linear algebra that can be useful in a broader (applied) scientific context. Much attention will be given to recognising problems and applying correct mathematical techniques for solving, or at least a correct formulation of the problem in order to be able to solve it (by e.g. using computers). The students have to acquire the formal language of mathematics. The correct mathematical expression of certain concepts will be regarded as important.
Participating in the college will require active contribution by the students, e.g. in turns they will have to present the solution of their exercises on the blackboard; the end goal being that the students are considered to be able to present their results in an orderly fashion before their peers.
I. Introduction: Vectors, real vector spaces, lineare (in)dependence and span, bases, coördinates
II. Matrices: addition, scalar multiplication, internal multiplication,, regular and singular matrices
III. Determinants, main determinant, rank
IV. Solving systems of equations by means of the methods of Gauss-Jordan and Cramer
V. Vector geometry in the plane and the space, lines and planes and their relative position, collinearity en coplanarity
VI. Euclidean spaces, scalar and vector product, length, angle, orthogonality
VII. Linear transformations, kernel, image, original, eigenvectors en eigenvalues
Introduction to Maple