Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(10 p.) 8. Let B = {1,..., un} be a basis of a vector space V over F. For each 1

(10 p.) 8. Let B = {1,..., un} be a basis of a vector space V over F. For each 1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 18E
See similar textbooks
icon
Related questions
Question

8

(10 p.) 8. Let B = {1,..., un} be a basis of a vector space V over F. For each 1<i<n set v=eol ]B. Thus v Є V* is given by the formula v (u) = ci, where [u]B = Cn EF is the B-coordinate vector of u. Show that the set B* = {v,..., v} is a basis for V* (called the basis dual to the basis B).
Transcribed Image Text:(10 p.) 8. Let B = {1,..., un} be a basis of a vector space V over F. For each 1<i<n set v=eol ]B. Thus v Є V* is given by the formula v (u) = ci, where [u]B = Cn EF is the B-coordinate vector of u. Show that the set B* = {v,..., v} is a basis for V* (called the basis dual to the basis B).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS