Math 333 - Linear Algebra
Final Exam Review
Fall 2007
1 Sections Covered
The final exam will have two parts. The first part will be cumulative, covering material
from the first two exams. The second part will cover the material we have learned since
the last exam.
For Part 1, you should go over the review sheets and practice exams for the first two
exams. This time around it will be mostly computational, but you are expected to know all
definitions and theorems mentioned on those review sheets. The proofs will be emphasized
significantly less on this part of the final exam.
Part 2 of the final exam will cover Sections 3.1-3.4, 4.1-4.4, and 5.1-5.2 of the textbook.
You should read and understand all of these sections.
2 Definitions
You should know ALL definitions covered in the above mentioned sections, not just those
listed below. However, you should 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,
“an eigenvalue λof a matrix Ais any root of the characteristic polynomial det(A−λI) = 0”
is NOT the definition; it is a theorem.
1. Chapter 3: Elementary row operations, Augmented matrix, Homogeneous and In-
homogeneous systems, Consistent system, Row echelon form, Reduced row echelon
form.
2. Chapter 5: Diagonalizable matrix and linear transformation, eigenvalue/eigenvector
of a matrix and linear transformation, eigenspace, characteristic polynomial, algebraic
multiplicity, geometric multiplicity.
For Sections 5.1 and 5.2, many definitions are given in the book in terms of linear
transformations, but in class the definitions were given in terms of matrices. If you are asked
for the definition of something involving matrices, then I want you to write a definition IN
TERMS OF MATRICES, and there should be NO MENTION of a linear transformation
(and vice versa). For example, for the definition of “Diagonalizable matrix”, you should
NOT say,
“The square matrix Ais diagonalizable if the linear transformation LAis diag-
onalizable.”
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