Problem 6 - [10] Let V be a normed vector space. Show that ||x – y|| = ||x – z|| + ||z – yll V x, y, ze V. Problem 7 - [

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Problem 6 10 Let V Be A Normed Vector Space Show That X Y X Z Z Yll V X Y Ze V Problem 7 1 (90.37 KiB) Viewed 92 times

Problem 6 - [10] Let V be a normed vector space. Show that ||x – y|| = ||x – z|| + ||z – yll V x, y, ze V. Problem 7 - [10] Let x and y be two generic elements of a normed space. Show that ||-|-|||| < |x-y|| Problem 8 [10] Let z and w be two complex number. Show that | z + ut slz + w. Obviously, this property is valid for real numbers as well, since RC C. Show then that if ze C, with z=a +ib, 11:11 = 1z1 = Va? +bis indeed a norm.