In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is 
Elementary Linear Algebra.  The book should have at least the following things

-- An online homework system
-- A good emphasis on proofs in the exercises
-- Should introduce linear transformations earlier
-- Some applications 

Any recommendations would be greatly appreciated. Thank you for your help