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The Cauchy-Schwarz inequality says that if a = (a1,.…, an) and b = (b1,..., b,) are two vectors in R", then Jā - õ| < |||- In this exercise you will give a proof of this inequality using multivariable calculus. (a) Assume that the inequality is true for all 5 e R" with ||õ|| = 1. Deduce from this that the inequality must then be true for all be R".

The Cauchy-Schwarz inequality says that if a = (a1,.…, an) and b = (b1,..., b,) are two vectors in R", then Jā - õ| < |||- In this exercise you will give a proof of this inequality using multivariable calculus. (a) Assume that the inequality is true for all 5 e R" with ||õ|| = 1. Deduce from this that the inequality must then be true for all be R".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q3. The Cauchy-Schwarz inequality says that if a = (a1,.…., an) and b = (b1,..., bn) are two vectors in R", then In this exercise you will give a proof of this inequality using multivariable calculus. (a) Assume that the inequality is true for all 5 E R" with ||b|| = 1. Deduce from this that the inequality must then be true for all b E R".
Transcribed Image Text:Q3. The Cauchy-Schwarz inequality says that if a = (a1,.…., an) and b = (b1,..., bn) are two vectors in R", then In this exercise you will give a proof of this inequality using multivariable calculus. (a) Assume that the inequality is true for all 5 E R" with ||b|| = 1. Deduce from this that the inequality must then be true for all b E R".
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