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

A = {{4.,7.,-3.},{2.,-4.,6.},{-3.,2.,5.},{1.,-2.,4.}}
b = {1.,5.,7.,-3.}
{Q, R} = QRDecomposition[A]
xt = LinearSolve[R,Q.b]
x = N[xt]
r = A.x-b
e = Transpose[A].r