When: Friday, May 1, as previously announced. (There will be some review in lecture Wednesday.)
Conditions:
Five problems, each for 10 points. One will consist of several brief-answer parts.
Please sit where assigned.
Closed book.
No bluebooks needed.
Calculators should not be needed, but are permitted, except for those that can do linear algebra.
Coverage:
Lectures through Monday, April 27.
Homework through Assignment #4, including problems ``not to hand in''. Most exam problems will resemble homework problems.
All handouts.
Reading from text: Sections 4.1, 4.2, 4.3, 4.4, 5.1, and 5.2 to the extent we get to it in lecture. You can omit any topics that were never mentioned in lecture or homework.
Proofs to know specifically:
(a) Theorem 4-2 (p. 188), (5) and (1) as in lecture. (If this is asked, the list of defining properties of a vector space (p. 181) will be provided; you need not memorize it.)
(b) Proofs that the following are subspaces: the span of a list of vectors, the nullspace of a matrix, the range and kernel of a linear transformation.
(c) The reason why the row space does not change when you do an elementary row operation.
(d) The reason for the uniqueness property of a basis, starting from the condition of being linearly independent and spanning.
In addition, know reasoning from homework problems.
Office Hours: Thursday, April 30, 1:00-2:00, instead of Friday.