6. Show that each of the following are not inner products on R³, (a) (u, v) = U₁V₁ + U2V2; (b) (u, v) = U₁v₂U3+ V1 U2 V3, 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+ V1 U2 V3, 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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Q6
Transcribed Image Text:6. Show that each of the following are not inner products on R³,
(a) (u, v) = U₁V₁ + U2 V 2 ;
1
(b) (u, v) = U₁V2U3 + V1 U2 V3,
for u = (U₁, U2, U3)ª and v
(V1, V2, V3)T.
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