Gaussian Elimination Examples

Gaussian Elimination Examples

Author: c o

To demonstrate Gaussian elimination through several examples.

After a brief preamble in which requisites are listed, three video examples demonstrate Gaussian elimination.

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In the spirit of the old dictum practice makes perfect, this packet works through several examples of Gaussian elimination and Gauss-Jordan elimination.  

It is hoped that, after viewing the examples, the learner will be comfortable enough with the technique to apply it to any matrix that might be presented.  

Before beginning, some necessary background can be found in this lesson on Solving Linear Systems and this packet on Gaussian Elimination.  

And now, the examples.

Example 1

The first example stops short of reaching a reduced row echelon form because it becomes clear that the system has no solutions.

Example 2

We reduce a 3x5 matrix to reduced row echelon form, and determine its free variables.

The video is blurry at the beginning, but clears up before any real calculation begins.

Example 2 - Follow Up

Example 3

A 3x6 matrix is reduced, its free variables are determined, and the set of its solutions is formulated.

The video starts off blurry, but clears up before we get to any real calculation.