https://studiegids.vu.nl/en/courses/2025-2026/X_400638After this course...the student is able to solve linear systems of equations.the student is able to invert matrices, and to characterise (non)invertible matrices.the student is able to compute the determinant of a matrix, and to use it in different linear algebra contexts.the student can apply the theory of vector spaces to linear algebra problems, can calculate a basis for (sub)spaces.the student can calculate the eigenvalues and eigenvectors of a matrix, can perform a diagonalisation, and can use these techniques to study linear difference equations.the student can orthogonalise a set of vectors, can work with inner products and norms, and can perform projections on subspaces.the student can show whether a quadratic form is positive or negative definite, and can perform a Singular Value Decomposition.the student can prove small linear algebra theorems in a logical mathematical argument.The following subjects will be covered in this course: solving systems of linear equations;linear (in)dependence;matrix operations;determinants;vector spaces and subspaces;basis and dimension of vector spaces;rank of a matrix, the rank theorem;coordinate systems and changes of basis;eigenvalues and eigenvectors;diagonalisation of matrices;QR factorisations of a matrix;inner product, length, orthogonality;orthogonal projections, method of least squares;symmetric matrices and their orthogonal diagonalisation;quadratic forms;singular value decomposition of a matrixEvery week there are two lectures and one exercise class, of two hours each.This course has two written exams, one in each period. Additionally, there are two short written tests made during the tutorials. You will have passed the course if you meet the following requirements:at least a 5.0 for the first exam;at least a 5.0 for the second exam;at least a 5.5 on average;The exams and the short tests together form your final grade as follows: 30% for exam 1, 50% for exam 2, 20% for the average of the short tests. Students that cannot or do not have to take part in the tutorials/short tests (as decided by the study advisor, for example part time students) receive their final grades as 40% for the first exam and 60% for the second. Your final grade is rounded to the nearest half point, taking into account that averages between 5.0 and 6.0 are rounded to the nearest integer. Resits: In case you failed the course, you need to take a resit to pass the course, an exam that covers the entire contents of the course. The short tests form 20% of your resit grade, if and only if this yields a higher final grade.David C. Lay, Stephen R. Lay and Judi J. McDonald, Linear Algebra and its Applications, 5th edition, Pearson Global Edition, ISBN-139781292092232Bachelor Mathematics Year 1, Bachelor EOR Year 1High school mathematics