# How to Extend and Calculate a Basis for the Whole Space

For example, say you start out with (2,1,0) and (2,0,2). Well the easiest answer here is to think of these two vectors in a plane, so you should take the cross product to get the vector that is not in the plane, and there you have a basis for R^3. But how about when we run into similar problems in R^n, not just when we are given n-1 vectors, but perhaps any m less than n. What would be the systematic method?