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					               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:
    Linear system
    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)
    Theorem 1
    Pivot position and pivot column
    Row reduction algorithm to REF and RREF
    Basic vs. free variables
    Parametric descriptions of solution sets
    Back Substitution
    Theorem 2

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
    Linear combinations
    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.
    Theorem 3
    Existence of solutions to Ax=b
      Theorem 4!!!!!!!!!
      Row-vector rule for computing Ax
      Theorem 5

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.
    Theorem 7
    Theorem 8
    Theorem 9

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.
    Matrix transformations
    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
    Theorem 11
    Theorem 12

      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
book).

				
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posted:10/31/2011
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