Let . Let . a) Prove that C is a cone and interpretate C geometrically (C is a cone if ). b) Suposse S is a close set. ¿Is C necessarely close? If not, ¿what are the conditions for him to be close? Thank you for every aportation.
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Well to prove that C is a cone, you must have your set containing the vectors for every . If so, then if u take any positive scalar , then is also in the set and hence your set is a cone by the definition of a cone.
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