Finding the Inverse Using the Gauss-Jordan Method:

To use the Gauss-Jordan Method, we have to augment "A" with the 5 by 5 identity matrix. Let's call the latter "I5":

> I5:=matrix(5,5,(m,n)->if (m=n) then 1 else 0 fi);

Now we augment "A" with "I5" and call the augmented matrix "AI":

> AI:=augment(A,I5);

If we use the Gauss-Jordan Method, the inverse of "A" will appear to the right of the partition:

> AIgj:=gaussjord(AI);

In order to extract the 5 by 5 inverse matrix from the 5 by 10 augmented matrix, we use Maple's "submatrix" command as follows:

> Ainv2:=submatrix(AIgj,1..5,6..10);

Let's check that this is the same inverse which was obtained before:

> evalm(Ainv-Ainv2);

We have agreement.

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