Gauss-Jordan Method for Calculating Inverse
by Joe McDonald

Hints

Rules

Practice Examples

STEP

AUTOMATIC MATRIX

ROW OPERATION

STEP 1

× ROW 1 2 3 Enter matrix in green(teal) area. Do indicated step. Calculation will appear in table below.

STEP 2

ROW 1 2 3 +  × ROW 1 2 3

STEP 3

ROW 1 2 3 +  × ROW 1 2 3

STEP 4

× ROW 1 2 3

STEP 5

ROW 1 2 3 +  × ROW 1 2 3

step6

ROW 1 2 3 +  × ROW 1 2 3

STEP 7

× ROW 1 2 3

STEP 8

ROW 1 2 3 +  × ROW 1 2 3

STEP 9

ROW 1 2 3 +  × ROW 1 2 3

The inverse is highlighted in green (teal):

If you multiply the original matrix by its inverse the product is :

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HINTS

• 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.

• 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 1 is not permitted when using this form. 

PRACTICE EXAMPLE

• Start with Example 1 on page 94

• Try this       or 

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada