1. Learning objectives: (PO: a, CGB1) - To solve systems of linear equations and to interpret the results. - To understand the concept of algebraic structure. - To know and understand the notion of vector spaces and their applications. - To understand the notion of bases and coordinates in a vector space. - To understand linear transformations and to represent them by matrices. - To compute the fundamental vector spaces associated to a matrix. - To understand the concept of eigenvalues and eigenvectors of a matrix, and to know their computation and applications. - To compute the QR decomposition of a matrix. - To find an approximate solution to an inconsistent system of linear equation by least-square fitting. - To obtain the singular value decomposition of a matrix. 2. Specific skills: (PO: a, CGB1) - To raise the abstraction level. - To be able to solve real problems using typical linear algebra tools. 3. General skills: (PO: a, CGB1) - To improve the oral and written communication ability using the language and signs of mathematics properly. - To be able to model a real situation described with words using mathematical concepts. - To improve the ability to interpret a mathematical solution and define its limitations and reliability. - To be able to use mathematical software.