(a) Prove that |x | a ll. (Hint: See Exercise 1.2.17.) (b) Prove that if b e R" is any vector, then b xk b a #4. Prove thata rectangle R = [a1, bi] x ...x [an, bn] C R" is closed. *5. Prove that the closed ball B (a, r) = {x e R" ||x - a|| < r} C R" is closed.
(a) Prove that |x | a ll. (Hint: See Exercise 1.2.17.) (b) Prove that if b e R" is any vector, then b xk b a #4. Prove thata rectangle R = [a1, bi] x ...x [an, bn] C R" is closed. *5. Prove that the closed ball B (a, r) = {x e R" ||x - a|| < r} C R" is closed.
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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I need help for number 4. Thanks!
![(a) Prove that |x | a ll. (Hint: See Exercise 1.2.17.)
(b) Prove that if b e R" is any vector, then b xk b a
#4. Prove thata rectangle R = [a1, bi] x ...x [an, bn] C R" is closed.
*5. Prove that the closed ball B (a, r) = {x e R" ||x - a|| < r} C R" is closed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a3b0a85-5819-488a-b640-64960995ba98%2F5619c533-8601-4e40-b6a8-662da4a708d0%2Fb7kso05.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Prove that |x | a ll. (Hint: See Exercise 1.2.17.)
(b) Prove that if b e R" is any vector, then b xk b a
#4. Prove thata rectangle R = [a1, bi] x ...x [an, bn] C R" is closed.
*5. Prove that the closed ball B (a, r) = {x e R" ||x - a|| < r} C R" is closed.
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