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.Use fractions 2/3 etc...

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.

• You can use fractions.  Multiple 3 by 1/3 to get 1.  Multiply 2/3 by 3/2 to get 1.  No mixed fractions like 3 2/3.

• 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.

It will convert decimals into fracions automatically.

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.