From: Adam Hall on
This comes from Introduction to Scientific Computing by Charles Van Loan...
I forget the edition, but the question is this:

% Implement the following function
% function [u,v] = Lines(a,b,c,d)
%
% a,b,c and d are column n-vectors with the property that for i=1:n, the
% lines
%
% x(t1) = a(i) + t1(b(i) - a(i)) -inf < t1 < inf
% y(t2) = c(i) + t2(d(i) - c(i)) -inf < t2 < inf
%
% intersect. The points of intersection (u(i),v(i)) are returned in column
% n-vectors u and v.
%
% Your implementation should use Gaussian Elimination with partial pivoting
% to solve for the intersection points. It should be fully vectorized. (No loops necessary.)

I'm completely lost as to how to solve this. I know how to do it by hand, but writing a function that does it is proving a little more difficult.
Can anyone lead me in the right direction?
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