Example 5. Use Gauss-Jordan elimination to find the inverse of the matrix  .

Solution 5.

Enter the matrix  A  and create a 4 by 4 identity matrix and store it in the variable Iden.

Remark.  In Mathematica the letter    is a reserved word which is used for the complex unit, i.e.  .  For this reason, we used the word    for our "identity matrix"  .  

Form the augmented matrix  .  using the following steps.

Then perform Gauss-Jordan elimination.

Use Mathematica to get the inverse of  A  out of  this augmented matrix, and store it in the matrix  B.

Verify the solution.

Notice.  
Since integers were entered as the matrix and vector elements, precise arithmetic with fractions was performed for all of the computations.  If you prefer the numerical approximations, then enter decimal entries or make the final answer numerical with the command:

Aside.  
Compare with Mathematica's "Inverse" procedure for finding the inverse of a matrix.

(c) John H. Mathews 2004