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Exercise 1 Some exercises on the Week 10 exercise sheet will give you all the...

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Algebra

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Exercise 1 Some exercises on the Week 10 exercise sheet will give you all the tools you need for this roblem You should work through those exercises but you can use them without including proofs of them Let b 2 2 and b 4 4 1 Is Bo b b2 a basis of Z 2 Let B spanz Bo Prove that B is a free abelian group of rank 2 3 Find a basis B b b of B a basis y c c of Z and positive integers d d2 such that b d c and b d c 4 Express Z2 B as a direct product of cyclic groups

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