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Show that the function (V1, V₂) = 2w1W2 + x1x2 - Y1Y2 +2122 defined for any vectors V₁ = (x1, y1, 21, W₁) and v₂ = (x2, Y2, 22, W2) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).

Show that the function (V1, V₂) = 2w1W2 + x1x2 - Y1Y2 +2122 defined for any vectors V₁ = (x1, y1, 21, W₁) and v₂ = (x2, Y2, 22, W2) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).

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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Show that the function (V1, V2) = 2w₁ W2 + X1 X2 - Y1Y2 + Z122 defined for any vectors V₁ = (x1, y₁, 2₁,w₁) and v₂ = (x2, Y2, 22, w₂) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).
Transcribed Image Text:Show that the function (V1, V2) = 2w₁ W2 + X1 X2 - Y1Y2 + Z122 defined for any vectors V₁ = (x1, y₁, 2₁,w₁) and v₂ = (x2, Y2, 22, w₂) in vector space R4 is not an inner product. Hint. Indicate which axiom(s) of inner product space is (are) not satisfied and give an example of the vector(s) which do(es) not satisfy the axiom(s).
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