1. Upper-Triangular Linear Systems
Definition 1.1 An NxN matrix A = (ai,j) is called upper-triangular provided that the elements satisfy ai,j = 0 whenever i > j. The matrix A = (ai,j) is called lower-triangular provided that ai,j = 0 whenever i < j.
x1 + 2x2 + x3 + 4x4 = b1 -4x1 + 2x3 -5x4 = b2 -5x3 -7.5x4 = b3