(b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by | 2 0.] (This is known as the Cauchy-Schwarz Inequality) (c) Show that ||x+y|| < ||x||+||y||. [Hint: Compute (x+y) · (x+y) and apply part (b).] (d) Show that d is a metric.
(b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by | 2 0.] (This is known as the Cauchy-Schwarz Inequality) (c) Show that ||x+y|| < ||x||+||y||. [Hint: Compute (x+y) · (x+y) and apply part (b).] (d) Show that d is a metric.
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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![(b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact
that ||ax + by | 2 0.] (This is known as the Cauchy-Schwarz Inequality)
(c) Show that ||x+y|| < ||x||+||y||. [Hint: Compute (x+y) · (x+y) and apply part (b).]
(d) Show that d is a metric.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b0185de-0645-4c2a-aea4-e046d61ab5cb%2F64dae52f-03d2-4dd0-8378-4b4fe1e68e49%2Favnj53n.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact
that ||ax + by | 2 0.] (This is known as the Cauchy-Schwarz Inequality)
(c) Show that ||x+y|| < ||x||+||y||. [Hint: Compute (x+y) · (x+y) and apply part (b).]
(d) Show that d is a metric.
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