function x = backsubs(R,b)
% FUNCTION x = backsubs(R,b)
% solve the system Rx = b given that R is 
% upper triangular. 
% INPUT:  R -- upper triangular m x n matrix 
%         b -- m x 1 vector
% OUTPUT: x -- n x 1 vector satisfying Rx = b
  
  [m,n] = size(R);
  x = zeros(n,1);
  
  x(n) = b(n)/R(n,n);
  
  for j = n-1:-1:1
    x(j) = (b(j)-R(j,j+1:n)*x(j+1:end))/R(j,j);
  end