**Department of Applied Mathematics**

**
Fall 2000 - Academic year 5761**

## Linear Algebra 1

### Room: ... - Sun 18:00 - 19:30

**Teacher Assistants**: Nathan Friedman and Adi Yarden.

**Syllabus:**

- Systems of n linear equations in p unknowns. The matrices attached to a
system of linear equations. Row operations. The Gauss-Jordan algorithm.
- Vector spaces, scalar product of vectors. Vector subspace.
- Linear dependence and independence of vectors. Genertaing sets of a vector space. Bases of a vector space, dimension of a vector space. The incomplete basis theorem.
- Linear operators. The matrix of a linear operator with respect to given bases. Properties.
- Important examples of linear operators: projectors, rotations, etc.
- Kernel and image of a linear operator, and their properties.
- The algebra of matrices; invertible matrices, computation of the inverse.
- The determinant of a square matrix and its properties. Cramer's method of resolution of a system of linear equations.

**Grading:**

The grade will be determined by final
exam (85%) and weekly home work assignements (15%).

**Course Text:**

Help Material for a Course in Linear Algebra,
Version 1.2, by A. Naimark (Translated and edited by Th. Dana-Picard; exercises by TDP and E. Reisin).
**Recommended Texts:**

- J.B. Fraleigh and R.A. Beauregard: Linear Algebra 3/e, Addison-Wesley (1995).
- C.W. Curtis: Linear Algebra: An Introductory Approach, Springer Verlag (1991)
- S. Amitsur: Algebra 1, Akademon, Jerusalem (in Hebrew).

** A tutorial for the course **

is available in two formats: Linux/Unix and Windows. Enjoy it.

** Solution sheets:**

Solutions for homework assignements will be available here, generally within one week. You're invited to use them.
The files are Postscript files.
If you work with Unix/Linux and have Ghostview installed, the solution file will be opened automatically in a separate window;

If you need a previewer under Windows, you can download the executable file , run it and it will install GSview (think of it as Ghostview for Windows). If needed, you can get more information on GSview and more information on how to configure it as a viewer for Netscape Navigator.

**Useful links:**

We hope that you will enjoy the course.

**Mathematical gems:**

If you are fond of mathematical gems, here is a note about very special balls. It needs only some linear algebra, with a little knowledge about distances.