Matrix Reduction Process

This section details the step-by-step process of reducing matrices and solving systems through elimination techniques.

Definition: Matrix reduction involves systematically eliminating variables to create a triangular system of equations.

Highlight: The process involves choosing equations and applying reduction techniques to eliminate variables systematically.

Example: A practical demonstration shows how to:

1. Select two equations from the system
2. Apply reduction to eliminate variables
3. Repeat the process with different equation pairs

Introduction to 3x3 Linear Systems

This page introduces the fundamental concepts of solving 3x3 linear systems through the Gaussian elimination method. The content focuses on transforming a system of three equations into an echelon form for easier solving.

Definition: A 3x3 linear system consists of three equations with three unknowns (x, y, z) that need to be solved simultaneously.

Highlight: The main objective is to transform the system into an echelon form where equations progressively contain fewer variables.

Example: The process starts with three equations and reduces them to:

• 3 unknowns (ax + by + cz = k)
• 2 unknowns (by + cz = k')
• 1 unknown (cz = k")

Vocabulary: Gaussian elimination (Método de Gauss) is a systematic method for solving linear systems by reducing them to row echelon form.