Function to find solutions to Ax=b

I'm trying to code a function that will solve the linear system of equations Ax=b for a matrix A that is m by n.

The approche is to basicly make your own rref() to find the solution to Ax=b, however the way I've done it only allows for a correct solution shen A is m by m.

So, my question is how do I go about to have the function work A is m by n?

I get the error:

Index in position 1 exceeds array bounds (must not exceed 3).

Error in mygauss (line 15)

augA(col_i,:) = augA(col_i,:) - augA(row_i,:)*augA(col_i,row_i);

The "must not exceed #" is depending on dimension m of A.

function x = mygauss(A,b)
%--------- OUTPUT ----------
% x  : the solution to Ax=b
%--------- INPUT -----------
% A  : a m by n matrix
% b  : a m by 1 vector
%---------------------------
augA = [A b];
[m,n] = size(A);

for row_i = 1:m
    augA(row_i,:) = augA(row_i,:)/augA(row_i,row_i);
    for col_i = 1:n
        if row_i ~= col_i
           augA(col_i,:) = augA(col_i,:) - augA(row_i,:)*augA(col_i,row_i);
        end
    end
end
x = augA(:,n+1);
end 

Answer 1

[aara]

You must consider when the matrix A has more columns than elements (n>m). From lines 12 to 15 (shown below) would use col_i for a row index and cause you the error:

    for col_i = 1:n
        if row_i ~= col_i
           augA(col_i,:) = augA(col_i,:) - augA(row_i,:)*augA(col_i,row_i);
           %in the line above, if number of columns is more than number of rows in matrix A you would 
           %exceed row dimensions of A.
        end

I hope this helps

[Isac Eriksson]

Thanks! that gave me some needed insight. The issue seems to be with line 13

    for col_i = 1:n

The avriable col_i (column index) through me off. I thought sence it was the column n I was working with that col_i would need to go from 1 to the number of columns n. col_i is in fact just the indicator of the column position. Therfore the correct line of code is;

        for col_i = 1:m