Answered: 2.4. Let V be a vector space and let…

2.4. Let V be a vector space and let v1, V2,..., Vn be a basis in V. For x = Ek=1 akVk, y = Prove that (x, y) defines an inner product in V. E-1 BiVk define (x, y) := E-1 akBr.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 24CM

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

2.4. Let V be a vector space and let v1, V2,..., Vn be a basis in V. For x =
Ek=1 akVk, y =
Prove that (x, y) defines an inner product in V.
E-1 BiVk define (x, y) := E-1 akBr.

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