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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
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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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.
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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