Page 2: Solving the System

The second page demonstrates the final steps of solving the system by substituting values back into the equations. This process, known as back-substitution, works from the bottom equation upward.

Example: The solution process yields: z = 3 y = 6 x = 5

Highlight: The back-substitution process begins with solving for z in the last equation, then uses this value to find y, and finally x.

Definition: Back-substitution is the process of solving for variables in reverse order, starting from the last equation in row echelon form.

Vocabulary: Normale Funktionsgleichung refers to the standard form of equations where variables are expressed explicitly.

Page 1: Setting Up the Gaussian Elimination Method

The first page introduces the fundamental setup and initial steps of the Gaussian elimination method. It begins with converting three linear equations into tabular form and demonstrates how to achieve row echelon form.

Definition: Gaussian elimination is a systematic method for solving systems of linear equations by converting them into row echelon form.

Example: The initial system of equations: x + 2y + 3z = 2 x + y + z = 2 3x + 3y + z = 0

Highlight: Two key operations are permitted in this method:

• Subtracting rows from each other
• Multiplying rows by constants

Vocabulary: Tabellenform (tabular form) refers to the organized arrangement of equations in a matrix-like structure.