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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MATH1850 Midterm 2 November, 2010 3 3. (total 9 marks) Answer each question in the space provided. For parts a – d, you do NOT have to show your work, but may choose to do so for part marks in case the final answer is wrong. You MUST show your work for part e. a)
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This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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

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