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Unformatted text preview: MA 265 GOINS SAMPLE MIDTERM EXAMINATION #2 Instructions: Circle the correct answer on the follow ing pages. You have 50 minutes to com plete 25 problems. No textbooks, personal notes, calculators, or computing aids are allowed during the examination period. Each problem is worth 4 points. This examination is worth 100 points. Name: 1 2 MA 265 MIDTERM #2 Chapter 4. Real Vector Spaces 4.1: Vectors in the Plane and in 3Space 1. Determine the tail of the vector bracketleftbigg 2 6 bracketrightbigg whose head is (1 , 2). A. (3 , 8) B. (1 , 4) C. ( − 1 , − 4) D. None of the above 2. Determine the head of the vector 2 4 − 1 whose tail is (3 , − 2 , 2). A. (1 , − 6 , 3) B. ( − 1 , 6 , − 3) C. (5 , 2 , 1) D. None of the above 3. For which pairs of points P and Q do we have −→ PQ = bracketleftbigg 5 − 1 bracketrightbigg ? i. P (1 , 1) and Q (6 , 0) ii. P (3 , 4) and Q (8 , 5) iii. P (2 , 3) and Q (5 , 2) A. (i) only B. (i) and (ii) C. (i), (ii), and (iii) D. None of the above 4.2: Vector Spaces 4. If V is a real vector space, then for every vector u in V , the scalar 0 times u gives the zero vector in V . A. True B. False 5. Let V be the set of positive real num bers. Define ⊕ by u ⊕ v = uv − 1 and ⊙ by c ⊙ v = v . Which of the following is true for all scalars c and d and all positive real numbers u and v ?...
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 Spring '10
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 Linear Algebra, Vector Space, Hilbert space, a. b. c., b. c. d.

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