General Information
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The exam will be held on Thursday, September 27, from 5:30pm to 7:00pm, in Smith Labs 154.
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Plan to arrive a few minutes early to allow time to distribute the exams.
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The exam will cover material from sections 1.1, 1.2, 1.3, 1.4, 1.5, and 1.6 in the text.
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Cell-phones should be turned OFF for the duration of the exam.
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You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
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This is a closed-book exam. No books or notes may be used during the exam.
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You will be expected to show all of your work. A correct answer with insufficient justification
may not receive full credit.
Topics
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Vector Spaces. (1.1) Know the definition of a vector space, and be able to prove that a given set (together with operations) is or is not a vector space. Be familiar with the vector spaces Rn, F(R), C(R), Pn(R).
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Subspaces. (1.2) Know the definition of a subspace of a vector space, and be able to determine whether or not a given subset of a vector space is a subspace.
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Linear Combinations. (1.3) Know the definition of a linear combination of a collection of vectors, as well as the span of a set of vectors.
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Linear Dependence and Independence. (1.4) Know the definition of linearly independence and be able to determine whether or not a given set of vectors is linearly independent.
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Solving Systems of Linear Equations. (1.5) Know how to solve a system of linear equations by reducing it to echelon form.
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Bases and Dimension. (1.6) Know how to find a basis for a given vector space
Important Definitions/Theorems/Axioms
I will expect you to know and be able to use all of the definitions, examples and theorems below to prove results similar to those on the homework assignments. You should know precise statements of the definitions and theorems in bold.
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Definition 1.1.1
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Example 1.2.2
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Example 1.1.3
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Proposition 1.1.6
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Example 1.2.3
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Definition 1.2.6
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Example 1.2.7
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Theorem 1.2.8
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Theorem 1.2.13
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Corollary 1.2.14
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Definition 1.3.1
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Theorem 1.3.4
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Definition 1.3.5
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Proposition 1.3.8
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Theorem 1.3.9
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Definition 1.4.2
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Definition 1.4.4
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Proposition 1.4.7
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Proposition 1.5.3
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Definition 1.5.6
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Definition 1.5.11
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Corollary 1.5.13
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Definition 1.6.1
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Definition 1.6.12
Preparing for the Exam
The exam will consist of questions similar to those on the homework assignments. Be sure you are familiar with how to solve these types of problems. I would also recommend using the following Chapter 1 Supplementary Exercises (p. 58) for practice: 1, 2, 3, 5, 6, 7, 8, 9, 11