MATH 201

Checklist  for  Test 2 (Wednesday, October 17, 2007)

The test will cover Chapter 3 and sections 4.1, 4.2. 
Understanding prior chapters is also important, but the problems will 
generally address topics from those chapters only indirectly. 

Concepts: 

- column space and nullspace of a matrix
- row reduced form (same as rref)
- rank of a matrix
- particular solution and general solution of Ax=b; "special" solutions
- independence and spanning
- basis and dimension
- orthogonal complement
- orthogonal projection

Skills:

- starting with a matrix, perform elimination to obtain rref
- finding particular solution and general solution of Ax=b (the latter is 
usually represented as an arbitrary linear combination of "special" solutions)
- determning rank of a matrix; this often involves finding the rref (R) or at 
least the echelon form (U), but sometimes can be guessed (and the guess justified)
- figuring out dimensions of various spaces, usually a column space 
or a nullspace of a matrix (this usually involves finding rank of some matrix)
- checking whether a set of vectors is independent
- finding bases of various spaces (again, usually a column space 
or a nullspace of a matrix)
- manipulations involving orthogonality of vectors or subspaces
- finding matrix of the orthogonal projection on a subspace

A "formula sheet" is allowed (one 8.5x11 page, handwritten, one-sided).
This is not supposed to be, and can not be, a substitute for 
understanding the concepts and learning the skills; it is supposed 
to help in understanding/learning by removing the need for memorizing 
technical details.

Finally, there will be additional office hours Tuesday afternoon,
1:30-3:30 (the day before the test)