Vector Worksheet - Math 205 A And B
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1
2Math 205 A & B
Quiz 05 ver01 page 1
02/28/2014
Name
1A. Let V be a vector space and let H be a subset of V . What three conditions must H satisfy in order to be a subspace
of V ?
1B. Recall F is the vector space of all continuous functions f : R → R. Let H be the subset of F consisting of all
functions f whose graphs have no points above the x axis. (So the graph of any member of H may have points right on the
x axis and/or below it).
Which parts of the definition of subspace (see (1A)) does this H satisfy? Which parts does it fail? Explain your answers!
(You may use good pictures).
THIS QUIZ CONTINUES ON THE OTHER SIDE!
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