Linear Algebra 1

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

Teacher: Dr Noah Dana-Picard (dana@mail.jct.ac.il) .

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:

Course Text:

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

Solution sheets:

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.

• Targil 1.
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• Targil 9.
• Targil 10.
• Targil 11.
• Targil 12.

Useful links:

• On-line exercises, by Prof. Gang Xiao at the University of Nice (France).
• The Mathematical Atlas.

Mathematical gems: