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Fall 2010 Midterm #2 Solutions (Ilona's class)

# Fall 2010 Midterm #2 Solutions (Ilona's class) - MATH1850...

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MATH1850 Midterm 2 November, 2010 2 1. (6 marks) Find the angle (in degrees) between the two vectors (4, 1, -2) and (5,-3,1). Hint: ) cos( v u v u 2. (2 marks each; 4 marks total) Answer each question in the space provided. a) Consider the set W consisting of all vectors of the form (a, b, 0) where a and b are real numbers and 0 a . Explain why the following vector space property fails. “For each u in V , there is an object u in V , called the negative of u , such that 0 u u u u ) ( ) ( ”. b) Consider the set W consisting of all vectors of the form (a, b, 1) where a and b are real numbers. Show why the following vector space property fails. “If u and v are objects in V , then v u is in V .

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