Gauss-Jordan Method for Calculating Inverse
by Joe McDonald

 Hints Rules Practice Examples
 STEP AUTOMATIC MATRIX ROW OPERATION

STEP 1

× ROW

Enter matrix in green(teal) area. Do indicated step. Calculation will appear in table below.

STEP 2

ROW × ROW

STEP 3

ROW × ROW

STEP 4

× ROW

STEP 5

ROW × ROW

step6

ROW × ROW

STEP 7

× ROW

STEP 8

ROW × ROW

STEP 9

ROW × ROW

The inverse is highlighted in green (teal):

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

• 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.

 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

• Start with Example 1 on page 94

• Try this       o

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada