7Given the inner product space (R³(R),+,., °), wherexoy = 3x₁₁ + 2(x₂₁ + X₁/₂) + 3x₂3/₂ + 2x3V3, X = (X₁, X2, X3),Y = (V₁, V2,Y3)and the vectors u₁=(1,-2,1), u₂=(-1,2,0), u3=(1,-1,1), u4=(0,1,1).Find the linear mapping ƒ:R³ →R³, such that f(u₁)=(4,0,4), ƒ(u₂)=(-3,2,-3),f(u3)=(3,1,3), f(u4)=(0,3,0).

Answered: Image /qna-images/answer/13e76afb-cd46-4864-ad3c-b4cb33d0b9b1.jpg

7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3, X = (X₁, X₂, X3),Y = (₁,2,3) and the vectors u₁=(1,-2,1), u2=(-1,2,0), u3=(1,-1,1), u4=(0,1,1). Find the linear mapping ƒ:R³ →R³, such that ƒ (u₁)=(4,0,4), ƒ(u₂)=(-3,2,-3), f(u3)=(3,1,3), fƒ(u4)=(0,3,0).

7 Given the inner product space (R³(R),+,·,· ), where xoy = 3x₁y₁ + 2(x₂Y₁ + X₁Y₂) + 3x₂Y/₂ + 2x3V3, X = (X₁, X₂, X3),Y = (₁,2,3) and the vectors u₁=(1,-2,1), u2=(-1,2,0), u3=(1,-1,1), u4=(0,1,1). Find the linear mapping ƒ:R³ →R³, such that ƒ (u₁)=(4,0,4), ƒ(u₂)=(-3,2,-3), f(u3)=(3,1,3), fƒ(u4)=(0,3,0).

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.1: Vector In R^n

Problem 28E

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