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Problem 2: Let V be an inner product space. Let u, v € V. a.) Show that ||u+v|| = ||u|| + ||v|| if and only if there exists a positive real number c such that u = cv or v = cu. b.) Show that | ||u|| − ||v|| | ≤ ||u − v||. - The above inequality is called the reverse triangle inequality.

Problem 2: Let V be an inner product space. Let u, v € V. a.) Show that ||u+v|| = ||u|| + ||v|| if and only if there exists a positive real number c such that u = cv or v = cu. b.) Show that | ||u|| − ||v|| | ≤ ||u − v||. - The above inequality is called the reverse triangle inequality.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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Problem 2: Let V be an inner product space. Let u, v E V. a.) Show that ||u+v|| = ||u|| + ||v|| if and only if there exists a positive real number c such that u = cv or v = cu. b.) Show that | ||u|| − ||v|| | ≤ ||u − v||. The above inequality is called the reverse triangle inequality.
Transcribed Image Text:Problem 2: Let V be an inner product space. Let u, v E V. a.) Show that ||u+v|| = ||u|| + ||v|| if and only if there exists a positive real number c such that u = cv or v = cu. b.) Show that | ||u|| − ||v|| | ≤ ||u − v||. The above inequality is called the reverse triangle inequality.
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