Problem 1

>> a = [4 2 3 4 0; 3 2 0 0 0; 0 4 3 1 2; 2 5 1 3 2; 1 3 6 2 1]

a =

     4     2     3     4     0
     3     2     0     0     0
     0     4     3     1     2
     2     5     1     3     2
     1     3     6     2     1

>> b = [33; 7; 31; 37; 38]

b =

    33
     7
    31
    37
    38

>> ge2

x =

    1.0000
    2.0000
    3.0000
    4.0000
    5.0000


--Problems 2 - 4 output--

n = 5

n =

     5

type ge2

for j=1:n-1
  for i=j+1:n
    m=a(i,j)/a(j,j);
    for k=j:n
      a(i,k)=a(i,k)-m*a(j,k);
    end
    b(i)=b(i)-m*b(j);
  end
end

for i=n:-1:1
  for j=i+1:n
    b(i)=b(i)-a(i,j)*x(j)
  end
x(i) = b(i)/a(i,i);
x
end

type p3script

makeamatrix
c = ones(n,1)
x = ones(n,1)
b = a*c
origa = a
origb = b
ge2
rfe = ( max(abs(x-c)) ) / ( max(abs(x)) )
rbe = ( max(abs(origb-origa*x)) ) / ( max(abs(origb)) )
emf = rfe/rbe
type makeamatrix

for j=1:n
  for i=1:n
    a(i,j)=(0.9+0.1*i)^(j-1);
  end
end
p3script

c =

     1
     1
     1
     1
     1


x =

     1
     1
     1
     1
     1


b =

    5.0000
    6.1051
    7.4416
    9.0431
   10.9456

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   3.0045e-12


rbe =

   8.1145e-17


emf =

   3.7026e+04

n = 6

n =

     6

p3script

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   2.4351e-10


rbe =

   4.2739e-17


emf =

   5.6975e+06

n = 7

n =

     7

p3script

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   3.5403e-09


rbe =

   8.2482e-17


emf =

   4.2922e+07

n = 8

n =

     8

p3script

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   5.9323e-08


rbe =

   7.2338e-17


emf =

   8.2008e+08

n = 9

n =

     9

p3script

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   1.0888e-07


rbe =

   1.1521e-16


emf =

   9.4510e+08

n = 10

n =

    10

p3script

--snip--

x =

    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000
    1.0000


rfe =

   3.2020e-06


rbe =

   8.3579e-17


emf =

   3.8312e+10

n = 17

n =

    17

p3script

--snip--

x =

   -0.7335
   17.9175
  -75.9227
  217.3219
 -420.1458
  602.9043
 -652.3022
  550.3504
 -360.7017
  188.1066
  -74.7963
   24.7939
   -4.6746
    1.9940
    0.8794
    1.0091
    0.9997


rfe =

    1.0015


rbe =

   2.6285e-16


emf =

   3.8103e+15

diary off