Answered: 2. Let R3 be a real vector space, and u…

2. Let R3 be a real vector space, and u = (u1, u2, u3), v = (V1, v2, v3) E R", then show that < u, v >= U1.V1 + 2 u2.V2 + U3.V3 defines an inner product on R$.

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. Let R3 be a real vector space, and u = (u1, u2, u3), v =
= (v1, v2, v3) E R",
then show that
< u, v >= U1.V1 + 2 u2.V2 + U3.V3
defines an inner product on R$.

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