# Linear Algebra: Theory and Applications
# Ward Cheney & David Kincaid
# JBPub.com (c) 2008 
# File: exp8211.map
# Example 8.2.11

with(LinearAlgebra):
A := Matrix([[4,7,-3],[2,-4,6],[-3,2,5],[1,-2,4]]);
b := Vector([1.,5.,7.,-3.]);
(Q,R) := QRDecomposition(A);
xt := LinearSolve(R,Transpose(Q).b);
x := evalf(LeastSquares(A,b));
r := A.x-b;
e := Transpose(A).r;