Example 4. Use the Gauss-Jordan elimination method to solve the linear system  .  

Solution 4.

Form the augmented matrix    using Mathematica's procedure AppendRows, which adds more elements to each of the rows, hence is a command to "append" column(s).  First, load the "MatrixManipulation" procedure into memory.  Be sure to execute the following command before any reference to "AppendRows" is made, otherwise a "multiple contexts" error will be committed.

Then perform Gauss-Jordan elimination. Note that we are storing the solution returned in the variable  G.

This time use Mathematica to get the solution vector    out of this augmented matrix !

Verify the solution.

We are done.

Aside.  We can compare our answer with the answer obtained by using Mathematica's built in  RowReduce  procedure.  

This agrees with our answer that was obtained with our subroutine GaussJordan[M,4].   

Aside.  We can compute the solution X with Mathematica's "LinearSolve" procedure.

(c) John H. Mathews 2004