# spanning sets and linear combinations in 2D

- Author:
- Shawn Godin

The sketch below shows that two non-parallel vectors (blue) and (red) span .
As a result, any other vector can be written as a linear combination of and , that is as for some .
Hence, in a sense, and define a co-ordinate system where we can define any point (by way of a position vector whose "co-ordinates" are ).