This example solves a linear least squares problem from
Linear Algebra, by R Bronson, Academic press.
using lud.
The example is in 5.4 example 4

A is 1  2  1
     3 -1  0
     2  1 -1
     1  2  2

b is  1
      2
      2
      1

This reduces to solving
transpose(A) A = transpose(A) b
using lud.

Bronson's result is 

x  0.7597
y  0.2607
z -0.1772

