Aha, yes. Computer languages borrowed the word 'vector', but they have basically nothing to do with the mathematical structure from linear algebra. It's best to keep them completely separate in your mind.
If a coordinates are given, then they will be given with respect to a basis. However, it's entirely possible to do things more abstractly without introducing coordinates and bases to begin with, for example:
Ok, I understand. But as used in computer languages, a vector can be simply 2 numbers. No coordinates or basis are implied. That's what I meant.