Program, Semester Week 7

Systems of Linear Equations

Linear equations appear very often throughout the natural sciences. Sometimes several linear equations appear simultaneously and we have to find a solution that fits them all - we say that we are solving a system of linear equations. This week we will study how we can find all solutions to such systems and how the structure of such solutions looks. An important term that will be used in this connection is a matrix as well as its (reduced) row-echelon form, which turns out to be a particularly useful notation technique in this regard.

Key Terms

Systems of linear equations. Matrix \(\mathbf A\). Coefficient matrix. Augmented matrix. Gauss elimination and row operations. Reduced row-echelon form \(\mathrm{rref}(\mathbf A)\). Rank \(\rho(\mathbf A)\). Particular solution and general solution.

Preparation and Syllabus

This week will cover Sections 6.1 through 6.4 from Chapter [06 - Systems of linear equations]. Note that Section 6.5 in this chapter is not a part of our syllabus.

Exercises

Exercises for Long Day.

Exercises for Short Day.