Math 333 - Linear Algebra
Exam 1 Review
Fall 2007
1 Sections Covered
The exam will cover Sections 1.1-1.6 from the textbook. You should read and understand
all of these sections.
2 Definitions
You should know ALL definitions covered in the above mentioned sections. Pay special
attention to the definitions of each of the following terms. DEFINITELY KNOW (i.e.
MEMORIZE) THESE DEFINITIONS.... Also, if asked to give a definition of something,
you can NOT give a theorem. For example, the definition of a subspace is NOT a subset
of a vector space which is closed under the operations and contains the zero vector. This
is a theorem, not the definition.
Chapter 1: Subspaces, Linear combination, Linear independence, “V= span(S)” or
“Sgenerates V”, Basis, Dimension
3 Theorems
You should know the statements and understand the usefulness of all theorems in the above
mentioned sections. Pay special attention to each of the following theorems. You will NOT
be asked to write the precise statements of most of these theorems, so don’t attempt to
memorize exactly what they say. Simply know how to use them. However, you may be
asked to write the precise statement if it has a ** next to it.
Chapter 1: Theorems 1.3**, 1.8, 1.9, Cor. 1 and 2 (pg. 46-47), 1.11
4 Computations and other Exercises
You are responsible for knowing any homework exercise that has been assigned as well as
similar computational exercises. However, you may choose to focus on the following types.
1. Determine if a set Vis a vector space under specific operations.
2. Determine if a subset Wof a vector space Vis a subspace of V.
3. Determine if a subset Sof a vector space Vis a basis of V, and determine if a vector
v∈span(S).
4. Be able to do the following exercises from the textbook: Sec. 1.2: (9, 11), Sec. 1.4:
(13, 15), Sec. 1.5: (12), Sec. 1.6: (12).
1
