Example 1.  Use Gauss-Jordan elimination to find the inverse of the matrix  .  

Solution 1.

Enter the matrix  A  and the augmented matrix .  

Form the augmented matrix  .  

Not perform Gauss-Jordan elimination.

Get the inverse of  A  out of  this augmented matrix, and store it in the matrix  B.

Verify the solution.

We are done.  

Aside.  We can compare our result with Mathematica's built in procedure.  

Aside.  If decimals are required in the solution then decimal need to be used when entering the matrix.

Enter the matrix  A  and the augmented matrix .  

Form the augmented matrix  .  

Then perform Gauss-Jordan elimination.

Get the inverse of  A  out of  this augmented matrix, and store it in the matrix  B.

Remark.  What if you thought that the inverse only had 6 decimal places of accuracy.

Then you would use the following matrix.

Aside.  We can compare our result with Mathematica's built in procedure.  

Verify the solution.

This should not be too surprising if only 6 decimal places were available.

However, Mathematica carries out its internal computations in about 17 decimal places,  so there are really more digits that usually are not printed.

Get the inverse of  A  out of  this augmented matrix, and store it in the matrix  B.

Verify the solution.

Chop the values that are close to zero.

This is a lot closer to the "true identity matrix."

(c) John H. Mathews 2004