Linear Algebra a

Upon successful completion of the course, the student is able to solve systems of linear equations by the Gaussian elimination. The student knows how to represent the system of equations in a vector or matrix form and is also capable of analyzing its solutions. The student understands the concepts of the subspace of a Euclidean space, the basis vector and the dimension of the space. The student knows how to verify whether given vectors are linearly independent. The student can do basic matrix computations and knows how to compute the determinant and the inverse of a given square matrix. The student knows how to prove typical rules in matrix algebra and is able to justify the existence of inverse matrix by using elementary matrices. The student is also capable of computing eigenvalues and the corresponding eigenvectors. The student knows how to represent geometric problems in terms of vectors and to solve them with tools of linear algebra.
The student can apply linear algebra in the context of practical problems, for example, by applying the method of least squares. The student is able to compute by hand and also by computer.

Poole, David: Linear Algebra: A Modern Introduction. Pesonen, Martti: Lineaarialgebra a (lecture notes). Leon, Steven J.: Linear Algebra with Applications.

Prerequisites:
Long mathematics syllabus in high school, or equivalent initial knowledge.

Offering data:
This course is intended for the following student groups:
• mathematics majors,
• minor subject students,
• Open University students and lifelong learners.