how to code a matrix A, such that A = [aij ] is defined by aij = max(i, j)

i am trying to perform gaussian elimination with partial pivoting and scaling when n = 10. here is my code:

n = 10;
b = [1,1,1,1,1,1,1,1,1,1]'
p = (1:n)';          % initialize the pivoting vector
  s = max(abs(A'));     % compute the scale of each row
  for k = 1:(n-1)
    r = abs(A(p(k),k)/s(p(k)));
    kp = k;
    for i = (k+1):n
      t = abs(A(p(i),k)/s(p(i))); 
      if t > r,  r = t;  kp = i;  end
    end
    l = p(kp);  p(kp) = p(k);  p(k) = l;   % interchange p(kp) and p(k) 
    for i = (k+1):n
      A(p(i),k) = A(p(i),k)/A(p(k),k);
      for j = (k+1):n
        A(p(i),j) = A(p(i),j)-A(p(i),k)*A(p(k),j);
      end
    end
  end
  p                      % output the pivoting vector
  A                      % output the overwritten matrix

% Step 2: Forward subsitiution to solve  L*y = b, where 
%         L(i,j) = 0 for j>i; L(i,i) = 1;  L(i,j) = A(p(i),j) for i>j.

    y = zeros(n,1);        % initialize y to be a column vector
    y(1) = b(p(1));
    for i = 2:n
      y(i) = b(p(i));
      for j = 1:(i-1)
        y(i) = y(i)-A(p(i),j)*y(j);
      end
    end
    y                      % output y

% Step 3: Back subsitiution to solve  U*x = y
%         U(i,j) = A(p(i),j) for j>=i; U(i,j) = 0 for i>j.

    x = zeros(n,1);        % initialize x to be a column vector
    x(n) = y(n)/A(p(n),n);
    for i = (n-1):-1:1
      x(i) = y(i);
      for j = (i+1):n
        x(i) = x(i)-A(p(i),j)*x(j);
      end
      x(i) = x(i)/A(p(i),i);
    end
    x

I don't know how to write the code for my A matrix when A = [aij ] is defined by aij = max(i, j). Any suggestions? thanks

[Jan]

How is the question and the code related? In "max(i,j)", what is "i" and "j"? What's wrong with max(i,j)?

Answer 1

[Matt J]

A=max(1:n,(1:n).')

Answer 2

[Torsten]

A loop is the easiest way to define your matrix, I guess:

A = zeros(n);
for i = 1:n
  for j = 1:n
    A(i,j) = max(i,j)
  end
end