6.8 Linear Systems and Elementary Operations - Linear Algebra and Analytic Geometry

We use row elementary operations on the "incomplete" matrix associated with a system of linear equations to reduce it in echelon form. Such a procedure has a two-fold advantage in the analysis of the solutions of the system: it allows to establish whether the system has solutions and provides a simplified system with the same solutions as the initial one.

Course chapters:

0. Introduction

1. Vector Spaces

2. Geometrical interpretation: vectors (algebra)----points (geometry)

3. Geometrical interpretation: sum and product by scalars

4. Sub-Vector Spaces and Linear Combinations

5. Linear Dependence

6. Matrices

7. ....