GNU Octave, version 2.9.8 (i486-pc-linux-gnu).
Copyright (C) 2006 John W. Eaton.
This is free software; see the source code for copying conditions.
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FITNESS FOR A PARTICULAR PURPOSE.  For details, type `warranty'.

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------------------------------------------------
Part a) -- original matrix
------------------------------------------------
Ab =

   3.02000  -1.05000   2.53000  -1.61000
   4.33000   0.56000  -1.78000   7.23000
  -0.83000  -0.54000   1.47000  -3.38000

------------------------------------------------
Begin step 1
pivot =  3.0200
row(2) <- row(2) - 4.33/3.02 * row(1)
row(3) <- row(3) - -0.83/3.02 * row(1)
Ab =

   3.020000  -1.050000   2.530000  -1.610000
   0.010000   2.060000  -5.400000   9.530000
  -0.010000  -0.820000   2.150000  -3.810000

------------------------------------------------
Begin step 2
pivot =  2.0600
row(3) <- row(3) - -0.82/2.06 * row(2)
Ab =

   3.02000  -1.05000   2.53000  -1.61000
   0.01000   2.06000  -5.40000   9.53000
  -0.01000   0.00000  -0.01000   0.00000

------------------------------------------------
Backsubstitution
sol =

   1.08000
   4.63000
  -0.00000

residual =

   0.010100
   0.018600
  -0.010800

exact_solution =

   1.00000
   2.00000
  -1.00000

------------------------------------------------
Part b) -- changed A(1,1)
------------------------------------------------
Ab =

   3.01000  -1.05000   2.53000  -1.61000
   4.33000   0.56000  -1.78000   7.23000
  -0.83000  -0.54000   1.47000  -3.38000

------------------------------------------------
Begin step 1
pivot =  3.0100
row(2) <- row(2) - 4.33/3.01 * row(1)
row(3) <- row(3) - -0.83/3.01 * row(1)
Ab =

   3.01000  -1.05000   2.53000  -1.61000
  -0.00000   2.07000  -5.42000   9.55000
   0.01000  -0.83000   2.18000  -3.83000

------------------------------------------------
Begin step 2
pivot =  2.0700
row(3) <- row(3) - -0.83/2.07 * row(2)
Ab =

   3.01000  -1.05000   2.53000  -1.61000
  -0.00000   2.07000  -5.42000   9.55000
   0.01000  -0.00000   0.01000  -0.01000

------------------------------------------------
Backsubstitution
sol =

   1
   2
  -1

residual =

  -0.0100000
   0.0100000
   0.0100000

percentage_change =

    7.4074
   56.8035
       Inf

exact_solution =

   1.06001
   4.12536
  -0.18537

------------------------------------------------
Part c) -- changed b(3)
------------------------------------------------
b2 =

  -1.6100
   7.2300
  -3.3900

Ab =

   3.02000  -1.05000   2.53000  -1.61000
   4.33000   0.56000  -1.78000   7.23000
  -0.83000  -0.54000   1.47000  -3.39000

------------------------------------------------
Begin step 1
pivot =  3.0200
row(2) <- row(2) - 4.33/3.02 * row(1)
row(3) <- row(3) - -0.83/3.02 * row(1)
Ab =

   3.020000  -1.050000   2.530000  -1.610000
   0.010000   2.060000  -5.400000   9.530000
  -0.010000  -0.820000   2.150000  -3.820000

------------------------------------------------
Begin step 2
pivot =  2.0600
row(3) <- row(3) - -0.82/2.06 * row(2)
Ab =

   3.02000  -1.05000   2.53000  -1.61000
   0.01000   2.06000  -5.40000   9.53000
  -0.01000   0.00000  -0.01000  -0.01000

------------------------------------------------
Backsubstitution
sol =

   1.1500
   7.2500
   1.0000

residual =

   5.0000e-04
   1.6500e-02
  -1.1500e-02

percentage_change =

    6.4815
   56.5875
       Inf

exact_solution =

   1.1855
   8.6991
   1.5588