Understanding Gauss-Jordan Method for Solving Equations

Thread starter alnix
Start date Nov 23, 2013
Tags

Method

In summary, the Gauss-Jordan method is a mathematical technique for solving systems of linear equations by transforming the equations into an augmented matrix and using row operations to simplify it. The steps involved in using this method include writing the equations in standard form, creating an augmented matrix, reducing the matrix, and interpreting it to find the solutions. It differs from Gaussian elimination in the final step, as the reduced matrix is further simplified to obtain the solutions directly. The Gauss-Jordan method is most useful for solving systems of equations with a large number of variables or fractions/decimals. However, it has limitations in that it can only be used for linear equations and may not always be the most efficient method.

Nov 23, 2013

alnix

can someone explain me in detail or simply how Gauss-Jordan way of solving equations works? thanks.

Physics news on Phys.org

Nov 23, 2013

SteamKing

Staff Emeritus

Science Advisor

Homework Helper

There are many articles on the web illustrating this procedure. All you have to do is google them and take yer pick.

Here are two (one to read and one video):

http://en.wikipedia.org/wiki/Gaussian_elimination

Last edited by a moderator: Sep 25, 2014

Related to Understanding Gauss-Jordan Method for Solving Equations

What is the Gauss-Jordan method?

The Gauss-Jordan method is a mathematical technique used to solve systems of linear equations. It involves transforming the coefficients and constants of the equations into an augmented matrix and then using row operations to reduce the matrix to a form where the solutions can be easily obtained.

What are the steps involved in using the Gauss-Jordan method?

The steps involved in using the Gauss-Jordan method are as follows:

Write the equations in standard form.
Create an augmented matrix by placing the coefficients and constants of the equations in a rectangular grid.
Use row operations to reduce the matrix to a form where the solutions can be easily obtained.
Interpret the reduced matrix to find the solutions to the equations.

What is the difference between Gauss-Jordan method and Gaussian elimination method?

Both the Gauss-Jordan method and Gaussian elimination method are used to solve systems of linear equations, but they differ in the final step of obtaining the solutions. In Gaussian elimination, the reduced matrix is interpreted to find the solutions, while in Gauss-Jordan method, the reduced matrix is further simplified to obtain the solutions directly.

When is the Gauss-Jordan method most useful?

The Gauss-Jordan method is most useful when there are a large number of equations and variables involved. It is also helpful when solving systems of equations with fractions or decimals, as it eliminates the need for fraction/decimal manipulation.

What are the limitations of the Gauss-Jordan method?

The Gauss-Jordan method is limited to solving systems of linear equations. It cannot be used for non-linear equations or equations with complex numbers. Additionally, it may not always be the most efficient method for solving equations, as it involves multiple steps and calculations.