Task I.V. Proskuryakova - the result of many years of experience of employees of the Department of Higher Mathematics, Faculty of Mechanics and Mathematics, Moscow University. It includes sections on determinants, systems of linear equations, matrices and quadratic forms, vector spaces, and their linear transformations. The collection contains typical computational problems for the use of basic algorithms of linear algebra, a large number of problems of increased difficulty, including theoretical ones. The most complex tasks are equipped not only with answers, but also with solutions. The textbook is intended for students of physical and mathematical, engineering, physical and economic and mathematical specialties of universities.