1. LetV = K". Show that V with the usual dot product is a scalar product. 2. Let V be a vector space with a scalar product. Let S be a subset of V. Define s* = {weV:=0 for all ve S}. Show S* is a...

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=0 for all ve S}. Show S* is a subspace of V. 3. Prove the Schwarz inequality: For all v, w e V, we have< v,="" w=""><|| v="" ||="" ||="" |.="" "/="">
Extracted text: 1. LetV = K". Show that V with the usual dot product is a scalar product. 2. Let V be a vector space with a scalar product. Let S be a subset of V. Define s* = {weV:< w,v="">=0 for all ve S}. Show S* is a subspace of V. 3. Prove the Schwarz inequality: For all v, w e V, we have< v,="" w=""><|| v="" ||="" ||="">