(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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.3: Change Of Basis

Problem 21EQ

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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.

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