We consider the system of linear equations or
To perform Gaussian elimination starting with the above given system of equations we compose the augmented matrix equation in the form:
After performing elementary raw operations the augmented matrix is put into the upper triangular form:
By using the formula:
Solve the equation of the kth row for xk, then substitute back into the equation of the (k-1)st row to obtain a solution for (k-1)st raw, and so on till k = 1.