# Linear Algebra I (MAY121)

### General

School School of Science Department of Mathematics Undergraduate MAY121 1 Linear Algebra I Lectures (Weekly Teaching Hours: 5, Credits: 7.5) General Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes After finishing the course, the students will be able: to use matrices as a tool in theoretical or numerical computations to compute the rank of a matrix to compute determinants to solve linear systems of equations to understand and use the notion of vector space. The aim of the course is to empower the graduate to analyse and compose basic notions and knowledge of Linear Algebra and advance his creative and productive thinking.

### Syllabus

• The algebra of (m x n) matrices and applications.
• Row echelon forms and reduced row echelon form of a matrix.
• Rank of a matrix. Determinants. Invertible matrices.
• Linear systems and applications.
• Vector spaces. Linear maps.
• The space L(E,F) of linear operations.
• Subspaces. Bases. Dimension. Rank of a linear operation.
• Fundamental equation of dimension and its applications. Matrix of a linear map. Matrix of a change of bases. The isomorphism between linear mapsand matrices. Equivalent matrices. Similar matrices. Determinant of an endomorphism. Sum and direct sum of vector subspaces.

### Teaching and Learning Methods - Evaluation

Delivery Classroom (face-to-face)
Use of Information and Communications Technology
• Teaching Material: Teaching material in electronic form available at the home page of the course.
• Communication with the students:
1. Office hours for the students (questions and problem solving).
2. Email correspondence
3. Weekly updates of the homepage of the course.
Teaching Methods