created 10/24/98; revised 08/01/00, 07/28/03, 07/25/09
A matrix and a column matrix can be multiplied together if their dimensions allow for it. This is a fundamental operation in computer graphics (and in many other fields). When a 3D graphics program is running the operation is performed millions of times per second.
You have seen several multiplication-like operations before:
What type of object (do you suppose) is the result of a matrix times a column matrix?