com08sA - AMS Common Exam Part A January 2008 Name ID Num...

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Unformatted text preview: AMS Common Exam - Part A, January 2008 Name: ID Num. Part A: / 75 Part B: / 75 Total: / 150 This component of the exam (Part A) consists of two sections (Linear Algebra and Advanced Calculus) with four problems in each. Each question is worth 25 points; choose THREE questions to answer from EACH section. Each problem should be solvable in approximately 20 minutes or less. Provide your answer in the space provided, and show all work. If extra sheets are used, place them inside the booklet and note on the cover page how many additional pages are included. Good Luck! Section 1: Linear Algebra Choose three of the four problems to solve. 1. Consider a parallelogram in R 3 with edges defined by the vectors ~x and ~ y , and a parallelepiped formed by vectors ~x , ~ y and ~ z . (a) Find an expression for the area of the parallelogram in terms of inner vector products. (b) Find an expression for the volume of the parallelepiped in similar terms. 2. Consider the set of functions of the form ae x...
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com08sA - AMS Common Exam Part A January 2008 Name ID Num...

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