linalghw1 - Check that all the axioms are satised if we let...

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1 homework 1, due wednesday, 4/13 in class, or in Vladimir’s box by 4:00pm 1. axler chapter 1 #2 , 4 , 5 , 10 , 13 2. Let U R 3 be the subspace U = { ( a,b,c ) such that a + b + c = 0 } . Find a basis of U , and prove that it is a basis using the definitions. 3. The definition of a vector space makes complete sense if we let the scalars ( F ) be the integers instead of the reals or the complexes (though you wouldn’t call that a vector space).
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Unformatted text preview: Check that all the axioms are satised if we let V be the example from class: V = { , v } , and addition is dened by + = , + v = v , v + = v , v + v = and multiplication by the integers by a = , a v = 0 if a is even, v is a is odd. Youll have to do that by cases. For instance, additive associativity has 8 possibilities. 1...
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