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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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