How to divide array, that result would be like dividing columns?

Hello, Can somebody give a little explanation about matrix division? For example there are two arrays a (100x5) and b (100x5). If I try to left divide two columns;

c=a(:,1)\b(:,1);

Result is c(1x1), However if I try to divide both arrays:

C=a\b;

Result is c(5x5), why it is not c(1x5)? As I understand it is different when dividing columns vs dividing matrix.

Answer 1

[Walter Roberson]

All combination of columns are used.

a(:,1)\b(:,1) a(:,1)\b(:,2) a(:,1)\b(:,3) ...
a(:,2)\b(:,1) a(:,2)\b(:,2) a(:,2)\b(:,3) ...

You could do

arrayfun(@(COL) A(:,COL)\B(:,COL), 1:size(A,2))