(*						      *)
(* Numerical Mathematics and Computing, Fifth Edition *)
(* Ward Cheney & David Kincaid		              *)
(* Brooks/Cole Publ. Co.			      *)
(* (c) 2004                                           *)
(* No warranties implied or expressed.	              *)
(* File: p_inv2  				      *)

(* finding the pseudoinverse of a matrix that has a deficiency in rank *)
MatrixForm[m = Table[{{-85, -55, -115}, {-35, 97, -167}, 
               {79, 56, 102}, {63, 57, 69},{45, -8, 97.5}}]]
MatrixForm[p = PseudoInverse[m, Tolerance->0.0001]]
MatrixForm[m.p.m]
MatrixForm[p.m.p]
m.p - Transpose[m.p]
p.m - Transpose[p.m]