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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![7
Given the inner product space (R³(R),+,., °), where
xoy = 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d74cef-f64d-4ed0-a004-41e9fb8cce2f%2F13e76afb-cd46-4864-ad3c-b4cb33d0b9b1%2Funtm0dt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7
Given the inner product space (R³(R),+,., °), where
xoy = 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).
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