two vector division algorithm

what algorithm goes when dividing two vectors? I.E. A= [1, 2, 3] and B= [4, 5, 6] and result of x = A/B would be 0.41558441558441. how come? I would like to write a method in c# to get this kind of result. i know that it is equivalent to x*A = B, but still it doesnt make it easier.

[Geoff Hayes]

Odre - see mrdivide which may provide an idea on the algorithm used to solve this problem.