Linear Algebra

2019-2020

Course Objective

After this course...

1. ...the student is able to solve linear systems of equations.
2. ...the student is able to invert matrices, and to characterise
(non)invertible matrices.
3. ...the student is able to compute the determinant of a matrix, and to
use it in different linear algebra contexts.
4. ...the student can apply the theory of vector spaces to linear
algebra problems, can calculate a basis for (sub)spaces.
5. ...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.
6. ...the student can orthogonalise a set of vectors, can work with
inner products and norms, and can perform projections on subspaces.
7. ...the student can show whether a quadratic form is positive or
negative definite, and can perform a Singular Value Decomposition.
8. ...the student can prove small linear algebra theorems in a logical
mathematical argument.

Course Content

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;
- LU and 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 matrix

Teaching Methods

Every week there are two lectures and one exercise class, of two hours
each.

Method of Assessment

This course has two written exams, one in each period.
The Mathematics student additionally have four 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;
- for Mathematics student: if you have attended at least 10 out of 14
tutorials.

The two exams and (for Mathematics students) the short tests together
form your final grade as follows:

a) for students in Econometrics & OR: 40% for exam 1 and 60% for exam 2.
b) for students in Mathematics: 30% for exam 1, 50% for exam 2, and 20%
for the average of the short tests.

Mathematics students that cannot or do not have to take part in the
tutorials (as decided by the study advisor, for example part time
students) receive their final grades using the rules for Econometrics &
OR students, so 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. For
mathematics students: the short tests form part of your resit grade, for
20%, if and only if this yields a higher final grade. For Econometrics &
OR students, only the resit exam counts towards your resit grade.

Entry Requirements

High school mathematics

Literature

David C. Lay, Stephen R. Lay and Judi J. McDonald, Linear Algebra and
its Applications, 5th edition, Pearson Global Edition,
ISBN-139781292092232

Target Audience

Bachelor Mathematics Year 1, Bachelor EOR Year 1

General Information

Course Code X_400638
Credits 6 EC
Period P1+2
Course Level 100
Language of Tuition English
Faculty Faculty of Science
Course Coordinator dr. R. Planque
Examiner prof. dr. A.C.M. Ran
Teaching Staff dr. R. Planque

Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: