Is the basis for the subspace W of a vectorspace V spanned by the basis of the vectorspace V? If so how?
For W < V, B_W (some basis of W) is linearly independent and spans W, therefore, there exists some B_V (basis of V) s.t. B_W < B_V.
I believe this is the basis extension theorem... not sure.
here is an example to think about. (1,0)n and (0,1) give a basis of R^2. now consider the subspace where y=x, i.e. the line at 45degrees through the origin. how woulkd you get a basis of that subspace from the given basis of R^2?