6. Show that each of the following are not inner products on R³, (a) (u, v) = U1v₁ + U₂V2; (b) (u, v) = U₁v2U3 + V₁U2V3, for u = (u₁, U2, U3)™ and v = (V₁, V2, V3)T.
6. Show that each of the following are not inner products on R³, (a) (u, v) = U1v₁ + U₂V2; (b) (u, v) = U₁v2U3 + V₁U2V3, for u = (u₁, U2, U3)™ and v = (V₁, V2, V3)T.
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
![6. Show that each of the following are not inner products on R³,
(a) (u, v) = U1v₁ + U2V2;
(b) (u, v) = U₁v2U3 + V₁U2V3,
for u = (u₁, U2, U3)¹ and v = (V₁, V2, V3)T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a97bb2c-6d83-4604-9a70-f559a7370826%2F650af9f7-97cb-42f3-b0a2-781a316412d8%2Fkyk6zr_processed.png&w=3840&q=75)
Transcribed Image Text:6. Show that each of the following are not inner products on R³,
(a) (u, v) = U1v₁ + U2V2;
(b) (u, v) = U₁v2U3 + V₁U2V3,
for u = (u₁, U2, U3)¹ and v = (V₁, V2, V3)T.
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