7. If Uj + 0 are components of a tensor of the type (0, 2) and if the equation fU¡j +gU ji= 0 holdsw.r.t to a basis then prove that eitherf=g and Uj is skew-symmetric orf=-g and Uij is symmetric.

Given : Uij≠0 ,fUij+gUji=0 To Prove : f=g , Uij is skew symmetric

7. If U¡¡ ‡ 0 are components of a tensor of the type (0, 2) and if the equation ƒU¡¡ + gU ji ³ = 0 holds ij w.r.t to a basis then prove that eitherf=g and Uij is skew-symmetric orf=-g and Uij is symmetric.

7. If U¡¡ ‡ 0 are components of a tensor of the type (0, 2) and if the equation ƒU¡¡ + gU ji ³ = 0 holds ij w.r.t to a basis then prove that eitherf=g and Uij is skew-symmetric orf=-g and Uij is symmetric.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.

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Question

7. If Uj + 0 are components of a tensor of the type (0, 2) and if the equation fU¡j +gU ji
= 0 holds
w.r.t to a basis then prove that eitherf=g and Uj is skew-symmetric orf=-g and Uij is symmetric.

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