Given a set of four vectors in space, prove that at least one is a linear combination of the other three. I think i am able to visualize this one in my head, but dont really know how to write a solid proof for it. Lets say i take any three of the vectors; The three will be either coplanar or non-coplanar. If they are coplanar, then any of those three vectors can be represented as a linear combination of the other two. If they are non-coplanar, then any vector in R^3 i.e. the fourth vector, can be be written as a linear combination of the three. Now i think i have visualised it correctly, but it certainly doesnt feel like i have proven much. Can anyone suggest how i could go about doing so? Thanks, Dan.