Gauss-Jordan Elimination
by Joe McDonald
NaN means Not a Number. You must enter numbers only and leave no empty cells.
Keep a calculator handy since this form does not handle fractions well. If you are trying to make 4 into 1, multiply by .25 etc... You may not be able to get a 1 exactly. 1.01 is close enough. Sometimes you need to experiment to get the correct number.
If you don't need to change an element just click No Action Required.
One way to always get a 1 is to multiply that row by the reciprocal of that number.
You must use decimal equivalents for this form.
One way to always get a 0 is to multiply a row with a 1 by the additive inverse of the number you want to make 0.
You must use decimal equivalents for this form.
Operation | Rule | Symbols |
Operation 1 |
Swap Rows: You can rearrange the equations (rows) in any order. | |
Operation 2 |
Multiply an equation (row) by a nonzero number | |
Operation 3 |
Add Rows: change an equation (row) by adding to it a multiple of another equation (row) |
Try the exercises 19 - 23 on page 60. This form works for 3 equations with 3 variables.
Try this First convert to augmented matrix form
There are 2 different levels to use this form.
Beginning: This is the default level. The row operations are pre-defined. The user only needs to supply the numbers (multiples) for each row operation.
Advanced: The user needs to supply the ROW numbers and the numbers (multiples) for each row operation.
Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada