For another example of what "scaling the matrix" means, here is the sample for the before and after scaling for the 3x3 matrix:
A=[ 1.8147 0.9134 0.2785
0.9058 1.6324 0.5469
0.1270 0.0975 1.9575 ];
b= [ 1.0 1.0 1.0 ]';
The result after making the matrix diagonaly dominant (+1) should be:
>> A2 = (Adiag(diag(A)))+ diag(sum(A'))+eye(3)
A2 = 4.0066 0.9134 0.2785
0.9058 4.0851 0.5469
0.1270 0.0975 3.1820