2. Let a € R be given. Define f: R" → R by f(x) = a¹x, x = R¹. Using the € - & definition, show that f is continuous. Hint: Use the Cauchy-Swhwarz inequality.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 19E
icon
Related questions
Question
2. Let a € R be given. Define f: R" → R by f(x) = a¹x, x = R¹.
Using the € - & definition, show that f is continuous. Hint: Use the
Cauchy-Swhwarz inequality.
Transcribed Image Text:2. Let a € R be given. Define f: R" → R by f(x) = a¹x, x = R¹. Using the € - & definition, show that f is continuous. Hint: Use the Cauchy-Swhwarz inequality.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage