midterm_2_sample - MA 265 GOINS SAMPLE MIDTERM EXAMINATION...

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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 3-Space 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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midterm_2_sample - MA 265 GOINS SAMPLE MIDTERM EXAMINATION...

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