Applet quiz on span and linear combinations
Definition of a vector; vector addition; scalar multiplication; visualization in R^2 and R^3; vector space axioms; linear combinations; span.
A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections.