-------------------------------
Part a)
-------------------------------
A =

  16  -28   0
  -28  53  10
   0  10  29

L =

  4  0  0
  -7  2  0
  0  5  2

residual =

  0
  0
  0

solution =

  -3
  -2
  2

-------------------------------
Part b)
-------------------------------
A =

   2.2500   3.0000   1.5000
   3.0000   6.2500   3.5000
   1.5000   3.5000   4.2500

L =

   1.50000   0.00000   0.00000
   2.00000   1.50000   0.00000
   1.00000   1.00000   1.50000

residual =

  0
  0
  0

solution =

  4
  -4
  4

-------------------------------
Part c)
-------------------------------
A =

   4  -2  -2   0
  -2   5   1  -2
  -2   1  10   3
   0  -2   3  18

L =

  2  0  0  0
  -1  2  0  0
  -1  0  3  0
  0  -1  1  4

residual =

  0
  0
  0
  0

solution =

  1
  -1
  1
  -1

-------------------------------
Part d)
-------------------------------
A =

   1  -2   3  -2
  -2  20  -2   8
   3  -2  11  -5
  -2   8  -5   9

L =

  1  0  0  0
  -2  4  0  0
  3  1  1  0
  -2  1  0  2

residual =

  0
  0
  0
  0

solution =

  -9.062500
   0.093750
   6.500000
  -2.375000