1A In the vector space (R²(R),+,-) find the values of the parameter dER, for which the mapping °: R² X R²R: (x,y) → x°y = x₁V₁ - 3(x₁₂ + x₂y₁) + dx₂y₂ where, x = (x1, x2), y = (y₁, y2) ER², defines an inner product in R². Then, for the appropriate values of the parameter dER, calculate the lengths of the vectors e₁ = (1,0), e2 = (0,1) and v = = (1,1), in terms of the previous inner product.
1A In the vector space (R²(R),+,-) find the values of the parameter dER, for which the mapping °: R² X R²R: (x,y) → x°y = x₁V₁ - 3(x₁₂ + x₂y₁) + dx₂y₂ where, x = (x1, x2), y = (y₁, y2) ER², defines an inner product in R². Then, for the appropriate values of the parameter dER, calculate the lengths of the vectors e₁ = (1,0), e2 = (0,1) and v = = (1,1), in terms of the previous inner product.
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
![1A
In the vector space (R²(R),+,-) find the values of the parameter deR, for which the mapping
°: R² XR² → R: (x,y) → xᵒy = x₁V₁ - 3(x₁V₂ + x₂V₁) + dx₂Y2
where, x = (x1, x2), y = (y1, y2) ≤R², defines an inner product in R². Then, for the appropriate values of the
(1,0), e₂ = (0,1) and v = (1,1), in terms of the
=
parameter d≤R, calculate the lengths of the vectors e₁
previous inner product.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d74cef-f64d-4ed0-a004-41e9fb8cce2f%2Fb0fa3d7c-72fb-405b-b9be-a05bc01d3139%2Fakkeis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1A
In the vector space (R²(R),+,-) find the values of the parameter deR, for which the mapping
°: R² XR² → R: (x,y) → xᵒy = x₁V₁ - 3(x₁V₂ + x₂V₁) + dx₂Y2
where, x = (x1, x2), y = (y1, y2) ≤R², defines an inner product in R². Then, for the appropriate values of the
(1,0), e₂ = (0,1) and v = (1,1), in terms of the
=
parameter d≤R, calculate the lengths of the vectors e₁
previous inner product.
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