The aim of this lecture is to introduce linear algebra and its applications to students of engineering faculty. The students, who complete the lecture successfully, can solve systems of linear equations by applying Gaussian elimination method, calculate determinants of matrices and apply them various problems of linear systems and vector calculus. Moreover, they can decide whether a given set is a vector space under an operation defined on the elements of the set and can find the dimension of a vector space. In addition, to these, they are able to find matrix representation of linear transformations, to calculate eigenvalues and eigenvectors of matrices and they can use them to diagonalize matrices. They are also capable of defining inner product and learn use it some fundamental calculations in vector spaces.

System of linear equations, Elementary row operations, Matrix algebra, Determinants, Vector spaces, Linear transformations, Eigenvalues, eigenvectors, Inner product spaces and its applications.