Upon completion of this course the student is able to:
- explain definitions and theorems of Linear Algebra and use them for solving exercises,
- explain and prove properties of vector spaces,
- recognize linear transformations, obtain the representation of linear transformations in the form of matrix-vector multiplication
- explain and prove properties of linear transformations,
- solve systems of linear equations in general form, and explain properties of the solution
- understand and give examples of applications of linear spaces.
Linear Structures I focuses on developing the theory and understanding the structure behind solving systems of linear equations. Such systems of linear equations form the basis for solving difference equations and differential equations, and have an enormous range of real-world applications, from|
mechanical systems to web search engines. The concepts that are discussed are vector spaces and related concepts such as linear subspaces; basis vectors; dimension; linear transformations; matrix-vector representation of linear transformations; null space; range; inverse transformation; solution set of a linear system; rank of a matrix; and determinant. The subject Linear Structures I lends itself well for first year students to experience the abstraction of mathematics. It is expected that the student learns to establish a correct mathematical proof for the properties of vector spaces and linear transformations.