What are the main steps in the GaussJordan algorithm to calc

What are the main steps in the Gauss-Jordan algorithm to calculate the inverse of a matrix [M] up to a dimension of 10 times 10? (Using the Gauss-Jordan algorithm and apply elementary row operations to [M] and the identity matrix (I) until [M] is reduced to |I|. then your original [I] will have become [M]-1) If you added \'pivoting\' to your algorithm how would it improve its applicability? How would you suggest improving the efficiency of the algorithm?

Solution

Gauss-jordan method: We can find the inverse of a non-singulsr matrix using elementary row operations only. This method is known as Gauss-jordan method

Working Rule : Suppose A is a non-singular square matrix of order n. we write A=InA. Now we apply elementary row operations only to the matrix A and the prefactor I_n of the R.H.S. We will do this till ew get an equation of the form

i.e I_n=BA, Then obviously B is the inverse of A.

Where I is a identity matrix