Problem Statement

A pascal matrix is a two-dimensional square matrix holding numbers from   Pascal's triangle,   also known as   binomial coefficients   and which can be shown as   nCr. Shown below are truncated   5-by-5   matrices   M[i, j]   for   i,j   in range   0..4. A Pascal upper-triangular matrix that is populated with   jCi: A Pascal lower-triangular matrix that is populated with   iCj   (the transpose of the upper-triangular matrix): A Pascal symmetric matrix that is populated with   i+jCi:

Write functions capable of generating each of the three forms of   n-by-n   matrices. Use those functions to display upper, lower, and symmetric Pascal   5-by-5   matrices on this page. The output should distinguish between different matrices and the rows of each matrix   (no showing a list of 25 numbers assuming the reader should split it into rows).

The   Cholesky decomposition   of a Pascal symmetric matrix is the Pascal lower-triangle matrix of the same size.

Let's start with the solution: