Gauss-Jordan Elimination
by Joe McDonald

 Hints Rules Practice Examples
 STEP AUTOMATIC MATRIX OPERATION MODE   Explanation of Mode STEP 1

� ROW

Enter matrix.  Do indicated step. Calculation will appear in table below.

Swap ROW with ROW STEP 2

ROW � ROW

Swap ROW with ROW STEP 3

ROW � ROW

Swap ROW with ROW STEP 4

� ROW

Swap ROW with ROW STEP 5

ROW � ROW

Swap ROW with ROW STEP 6

ROW � ROW

Swap ROW with ROW STEP 7

� ROW

Swap ROW with ROW STEP 8

ROW � ROW

Swap ROW with ROW STEP 9

ROW � ROW

Swap ROW with ROW

The solution is highlighted in navy blue.

Check solution in all 3 equations.

• 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.

RULES

 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) PRACTICE EXAMPLE

• 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 Explanation of Mode

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