Linear Algebra Study Guide for Exam 1
I really suggest that you make flashcards for all the important definitions in this course.
There is a lot of new terminology and you need to know what I (or the problem) is asking
you to do. This class is hard for students when they do not memorize the definitions. I
will ask you to define various terms and answer True/False questions based on the theory
(similar to your homework). You may use a scientific calculator only on Exam 1. No
graphing calculators will be allowed.
Section 1.1 You need to know the definitions for or how to do/use the following:
Solution to a linear system
Equivalent linear systems
Consistent linear systems
Inconsistent linear systems
Elementary row operations
Existence vs. uniqueness of a solution
Row reduce an augmented matrix to echelon form (REF)
Section 1.2 You need to know the definitions for or how to do/use the following:
Definition of Row Echelon form (REF) and Reduced Row Echelon Form (RREF)
Pivot position and pivot column
Row reduction algorithm to REF and RREF
Basic vs. free variables
Parametric descriptions of solution sets
Section 1.3 You need to know the definitions for or how to do/use the following:
Definition of a vector, equality of vectors, vector addition, scalar multiplication
Geometric descriptions of vectors in R2 and R3
Parallelogram rule for vector addition
Vectors in Rn
Algebraic properties of Rn
Solving vector equations using augmented matrices
Definition of a spanning set
Applications of linear combinations
Section 1.4 You need to know the definitions for or how to do/use the following:
Definition to multiply Ax on page 41.
Existence of solutions to Ax=b
Row-vector rule for computing Ax
Section 1.5 You need to know the definitions for or how to do/use the following:
Homogeneous linear systems
Trivial solutions vs. nontrivial solutions
How to determine if a homogeneous system has a nontrivial solution
Parametric vector form of the solution set
Theorem 6; understand the relationship between the solution to Ax=0 and Ax=b
Section 1.6 You need to know the definitions for or how to do the following:
Know how to do a problem like #1, #5 and #11.
Section 1.7 You need to know the definitions for or how to do/use the following:
Definition of linear independence – word for word!
Definition of linear dependence
How to tell if the columns of A are linearly independent
Linear independence relationships with a set of one or two vectors.
Section 1.8 You need to know the definitions for or how to do/use the following:
Definition of a transformation from Rn to Rm
Domain, co-domain and range.
Definition of a linear transformation (very important!)
Equations 3 and 4 on page 77
Be comfortable with all the new notation as well as terminology in this section.
Section 1.9 You need to know the definitions for or how to do/use the following:
Theorem 10 – very important!!!!!!!
Have a good understanding of tables 1, 2 and 3 on pp. 85-87.
Definition of an onto mapping
Definition of a 1-1 (one to one) mapping
Section 1.10 Anything out of this section would be put on a take-home part of
the exam. I may not even do that.
To study for the exam, know the above list of topics. Do your homework. Review your
quizzes. Do the supplementary exercises on pp. 102-104 (odds are in the back of the