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
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Chapter2: Second-order Linear Odes
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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.
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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