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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

Determine if the function defines an inner product on R², where u =
(u, v) = ₁V₁
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)
>
U
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) ≥ 0, and (v, v) = 0 if and only if v =
0
X
(U₁U₂) and v = (V₁, V₂). (Select all that apply.)

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Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3). ⟨u, v⟩ = u1v1 − u2v2 − u3v3
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