Matlab Function: Solving Ax=B using Gaussian Elimination where b is a n x m matrix not necessarily a n x 1 matrix.

So I was given the pseudocode to solve Ax=b when b is a n x 1 matrix (and thus x also is). I was able to successfully write a function that accomplished that. Now, I'm struggling to alter my function to solve Ax=b where b can now be a n x m matrix (A must be a n x n matrix, and x is an n x m matrix as result of b being a n x m matrix). I feel like the code must be pretty similar to consider this more general case but I can't seem to figure it out for some reason. Here's the code that I have:

function x = gaussianelim(A,b);

 [row,col]=size(A);

n = row;

x = zeros(n,1);

   for k=1:n-1   

    for i=k+1:n
        xMultiplier = A(i,k)/A(k,k);

        for j=k+1:n
            A(i,j) = A(i,j)-xMultiplier*A(k,j);

        end
        b(i) = b(i)-xMultiplier*b(k);
    end
    % backsubstitution:
    x(n) = b(n)/A(n,n);
    for i=n-1:-1:1
        summation = b(i);
        for j=i+1:n
            summation = summation-A(i,j)*x(j);
        end
        x(i) = summation/A(i,i);

    end

end

My code only works where b=nx1 matrix (and hence x is an nx1 matrix) but I need it to work when b is just an arbitrary n x m matrix. I would appreciate any help. Thank you.

[Akash tarpada]

can you please share the program?

Answer 1

[Jan]

[row,col] = size(A);
n = row;
x = zeros(size(b));
for k = 1:n-1   
  for i = k+1:n
     xMultiplier = A(i,k) / A(k,k);
     for j=k+1:n
        A(i,j) = A(i,j) - xMultiplier * A(k,j);
     end
     b(i, :) = b(i, :) - xMultiplier * b(k, :);
  end

% There is a missing "end" ?!   

    % backsubstitution:
    x(n, :) = b(n, :) / A(n,n);
    for i = n-1:-1:1
        summation = b(i, :);
        for j = i+1:n
            summation = summation - A(i,j) * x(j, :);
        end
        x(i, :) = summation / A(i,i);
    end

Simply replace x(i) by x(i, :) and the same for b.

[Li Guobin]

Hi

i encountered the same problem as Huskie. I tried the suggestion to replace X(i,j) by X(i,:) and it worked!

My question is why would the inner loop logic not work for "j"? Why is there a need to replace it with ":"?