# 1. Explain why the set M = {e,f,g} together with binary operations on M is a de

Posted: January 13th, 2023

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1. Explain why the set M = {e,f,g} together with binary operations on M is a defined table (picture) does not form a group? (I will sent a picture regarding to this question)

2. Let (G, ◦) be a group. Prove that in any row of the table for the group operation

◦ elements of G cannot be repeated. Does the same statement also apply to table columns?

3. In the vector space Z47 over Z7 you can find the basis of the subspace U ∩ V , where

U = span{(3,1,4,5)T, (2,2,1,6)T, (1,0,0,1)T}

and

V = span{(1,2,4,1)T, (2,6,6,3)T, (5,3,6,5)T}.

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