# Study unit

3315160 Vectors and matrices, 5 Cp
 Code 3315160 Validity 01.02.2021 - Name Vectors and matrices Abbreviation Vectors and mat Credits 5 Cp Date of expiry Type General Studies Subject 0510 Mathematics Class Study Unit Hours Study right Grading 0-5 Recommended scheduling Organisation Physics and Mathematics(J)

Teachers
Name
Janne Gröhn

Description
 Learning outcomes 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 is also capable of computing eigenvalues. The student knows how to represent geometric problems in terms of vectors and to solve them with tools of linear algebra. The student is able to prove basic properties of vectors and matrices by justifying each step of the argument. 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 symbolic software. Content Systems of linear equations and their solutions via Gaussian elimination, linear independence of vectors in a Euclidean space, subspace of a Euclidean space, basis vectors and dimension of a Euclidean space, straight lines and planes, matrices, determinant of a square matrix, eigenvalues and diagonalization, dot product of vectors, cross product of vectors and vector triple product. Modes of study This course is available only to M.Sc. (Tech.) students. Either course examination and active participation in exercises or general examination. Teaching methods Online material, small group sessions 14 h, exercises 14 h. Study materials Poole, David: Linear Algebra: A Modern Introduction (2nd ed.). Evaluation criteria 0-5 Teachers Janne Gröhn Prerequisites The basic studies in mathematics in university of applied science (tech.), long mathematics syllabus in high school or equivalent initial knowledge. Time Each year in period 4. Campus Campuses of Joensuu and Kuopio

Letter (J, K) in front of the name of the course/exam indicates the campus on which teaching or exam takes place: J = Joensuu, K = Kuopio.

Present and future teaching
Functions Name Type Cp Teacher Timetable
No registration in WebOodi Vectors and matrices  Lecture and exercise course  Janne Gröhn  21.03.22 -31.05.22

Future exams
Functions Name Type Cp Teacher Timetable
Registration not started Vectors and matrices  General examination  Janne Gröhn
 22.10.21 fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn
 14.01.22 fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn
 10.06.22 fri 12.00-16.00
Registration not started Vectors and matrices  General examination  Janne Gröhn
 26.08.22 fri 12.00-16.00