According to the structure of the textbook and typical academic syllabi, the core content includes:
for k = 1..n-1: find pivot row p with max |a[i,k]|, swap rows for i = k+1..n: m = a[i,k]/a[k,k] a[i,k:n] = a[i,k:n] - m * a[k,k:n] Numerical Analysis Titas Publication Pdf