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Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂). (Select all that apply.) (u, v)=81V₁+U₂V₁ + U₁V₂ + 8U₂V₂ satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) - (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v). does not satisfy c(u, v) = (cu, v) satisfies (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) 2 0, and (v, v) = 0 if and only if v=0

Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂). (Select all that apply.) (u, v)=81V₁+U₂V₁ + U₁V₂ + 8U₂V₂ satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) - (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v). does not satisfy c(u, v) = (cu, v) satisfies (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) 2 0, and (v, v) = 0 if and only if v=0

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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Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂). (Select all that apply.) (u, v) = ₁V1 + ₂V₁ + U1V2 +84₂V₂ satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) = (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v). does not satisfy c(u, v) = (cu, v) satisfies (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) 2 0, and (v, v) = 0 if and only if v=0
Transcribed Image Text:Determine if the function defines an inner product on R2, where u = (U₁, U₂) and v= (v₁, v₂). (Select all that apply.) (u, v) = ₁V1 + ₂V₁ + U1V2 +84₂V₂ satisfies (u, v) = (v, u) does not satisfy (u, v) = (v, u) satisfies (u, v + w) = (u, v) + (u, w) does not satisfy (u, v + w) = (u, v) + (u, w) satisfies c(u, v) = (cu, v). does not satisfy c(u, v) = (cu, v) satisfies (v, v) ≥ 0, and (v, v) = 0 if and only if v = 0 does not satisfy (v, v) 2 0, and (v, v) = 0 if and only if v=0
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