f = @(x) x.^5;
n = 5;



for i=0:n
  tarray(i+1) = i/n;
end
for j=1:(n+1)
   for i=1:(n+1)

       matrix(j,i) = tarray(i).^(j-1);
   end
end
matrix
for i=1:(n+1)
    matrixanswer(i) = f(tarray(i));
end
matrixanswer
matrixanswer = matrixanswer'
c = cond(matrix)
solution = matrix\matrixanswer
residualvector = (matrix*solution) - matrixanswer;

fprintf('The Condition of the Row-Based N=5 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector

for i=1:(n+1)

   for j=1:(n+1)

       matrix2(i,j) = tarray(i).^(j-1);

   end

end
for i=1:(n+1)

    matrixanswer2(i) = f(tarray(i));

end
matrixanswer2 = matrixanswer2';
c = cond(matrix2);
solution = matrix2\matrixanswer2;
residualvector = (matrix2*solution) - matrixanswer2;
fprintf('The Condition of the Column-Based N=5 matrix is %2.5f and the solution is\n', c);
solution
fprintf('And the Residual Vector is \n');
residualvector



% f = @(x) x.^5;
% n = 30;
% 
% 
% 
% for i=0:n
%   tarray(i+1) = i/n;
% end
% for j=1:(n+1)
%    for i=1:(n+1)
% 
%        matrix(j,i) = tarray(i).^(j-1);
%    end
% end
% matrix
% for i=1:(n+1)
%     matrixanswer(i) = f(tarray(i));
% end
% matrixanswer
% matrixanswer = matrixanswer'
% c = cond(matrix)
% solution = matrix\matrixanswer
% residualvector = (matrix*solution) - matrixanswer;
% 
% fprintf('The Condition of the Row-Based N=30 matrix is %2.5f and the solution is\n', c);
% solution
% fprintf('And the Residual Vector is \n');
% residualvector
% 
% for i=1:(n+1)
% 
%    for j=1:(n+1)
% 
%        matrix2(i,j) = tarray(i).^(j-1);
% 
%    end
% 
% end
% for i=1:(n+1)
% 
%     matrixanswer2(i) = f(tarray(i));
% 
% end
% matrixanswer2 = matrixanswer2';
% c = cond(matrix2);
% solution = matrix2\matrixanswer2;
% residualvector = (matrix2*solution) - matrixanswer2;
% fprintf('The Condition of the Column-Based N = 30 matrix is %2.5f and the solution is\n', c);
% solution
% fprintf('And the Residual Vector is \n');
% residualvector