Is there a difference between a linear dependent system and a spanning one? I've been confused about this for a while. Something is linearly dependent if it has a non trivial solution, and something is spanning if one of the vectors can be represented as a linear combination of another - implying there is a non-trivial solution- Some of my classmates told me i'm wrong, and I don't understand why. An explanation would be awesome. Can't seem to find anything online.