322first99

# 322first99 - = ac ad Do these operations turn Q × Q into a...

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Math 322 First Midterm Examination Name: April 8, 1999 Signature : 9:00–10:30 (1) Is 3 x 6 - 4 x + 6 irreducible in Z [ x ]? (10 points)

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(2) Does there exist a polynomial f in Z [ x ] such that f (0) = 1 , f (1) = 2, f (2) = 3, f (3) = - 2 ? (20 points)
Name : Surname : (3) For ( a, b ), ( c, d ) Q × Q and a Q , we put ( a, b ) + ( c, d ) = ( a + c, 0) and a · ( c, d

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Unformatted text preview: ) = ( ac, ad ). Do these operations turn Q × Q into a vector space over Q ? (20 points) (4) Find a feld K and a vector space V over K such that V has exactly 4 elements. (20 points) Name : Surname : (5) Why is the notion of dimension important? (30 points)...
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## This note was uploaded on 11/08/2011 for the course MATH 321 taught by Professor Ergenc during the Spring '11 term at Boğaziçi University.

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322first99 - = ac ad Do these operations turn Q × Q into a...

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