## Gauss-Jordan Elimination Program

**What it teaches:**

This program teaches the Gauss-Jordan elimination method of solving a system of linear equations. Here is a screen shot:

Because the program allows only elementary row operations and because it does the arithmetic, you can stay focused on the method and not get bogged down by the details.

**How it works:**

- You start with either a new system of 2, 3, or 4 equations, or you can open a previously saved system of equations.
- Once all the coefficients are entered, you can either click on
*Automatic*to go straight to the solution, or on*Manual*to solve the system yourself, step-by-step, by applying the three types of elementary row operations. - In Manual mode you can click on
*Assist*if you are stuck and the program will do the next step for you. - As the screen shot shows, you first test a row operation. The tentative result is shown in red below the row that will change. If this is what you intended then the operation is carried out. (The idea is that you can see the system of equations both before and after the operation.)

**Some ideas for teachers:**

- You can start with a solution and reverse the Gauss-Jordan procedure; thus creating a question in which your students will encounter only integers when they solve it.
- By letting the right side of a system of equations be (1, 0, 0), then (0, 1, 0), then

(0, 0, 1), you can explain the idea behind the inverse matrix.

**Where to now?**