Let V be a vector space.

Today we talked about how to turn a spanning set into a basis:

   Delete vectors you don't need.

   i.e.

   Delete vectors that are in the SPAN of prior vectors.  Your set
   will get smaller but it will still be a spanning set.


We also talked about how to turn a linearly-independent set into a basis:

   Add vectors you do need.

   i.e.
 
   As long as there is some vector in V that isn't in the SPAN of your
   set, just insert it into your linearly-independent set. Your set
   will get bigger but it will still be linearly-independent.

We did a number of examples on this.  Read the book for more examples.
Also read Ex 1-30  (Section 4.3) and turn in Ex 11, 12, 22.


If you need one of your test-grades to be curved, make sure to attend class.