Vectors and Matrices (5cr)

Objectives

After the course students can solve systems of linear equations using the Gaussian elimination. They are able present systems of linear equations in vector and matrix form and analyse the system’s solutions. They are familiar with subspaces of Euclidean spaces, the concepts of base and dimension. In particular, students are able to test if a given set of vectors is linearly independent. Students can use basic matrix operations, are able to calculate determinants, inverse matrices, as well as eigenvalues and eigenvectors of square matrices. Students can to represent various geometric problems using vector algebra and solve them using tools of linear vector algebra. They are able to prove properties of vectors and matrices, justifying each step of the proof. Students can model practical problems using linear algebra and solve them both by hand by using symbolic software. 

Content

Core contentSystems of linear equations: solving using Gaussian elimination. Linear independence of Euclidian space, subspaces, basis, rank, and dimension of subspaces of an Euclidian spaceDifferent techniques for describing lines and planesMatrices: matrix algebra, matrix product, transpose matrices, inverse matrices, determinant of matrices, eigenvalues and eigenvectors of matricesVectors: cross product, dot product and the vector triple product of vectorsUsing Matlab for vector and matrix calculations

Prerequisites

PREVIOUS STUDIES OR PREVIOUS KNOWLEDGE High School Mathematics OR Introduction to University Mathematics RECOMMENDED OPTIONAL STUDIES Prior to taking this course, it is recommended that students complete the Introductory Calculus OR Introduction to University Mathematics unless they have an excellent high school mathematics knowledge. Graduate students are advised to select the preceding course according to the recommendations/study guide of their degree programme.

Further information

This course belongs to the SEFI 1 level of engineering mathematics.