The manual is fully consistent with the program of the course "Analytical Geometry and Linear Algebra," provided for technical and economic universities with in-depth study of higher mathematics, such as MEPhI (Moscow Engineering Physics Institute). This manual discusses a large number of examples that contribute to the better assimilation of students this material. In addition, at the end of each chapter there is a list of tasks for self-solution that will help the reader control their knowledge. This book is based on manuals [1] - [3] (see the list of references). Operations [4] - [12] are recommended for additional reading of this course.