INNER PRODUCT SPACES 1. Let (u,v) be the Euclidean inner product on R², and let u = (2, -1), v= (-1,3), w = (0,-5) and k = -3. Verify that (a) (u,v) = (v,u) (b) (u +v, w) = (u,w) + (v,w) (c) (ku,v) = k(u,v)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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INNER PRODUCT SPACES
1. Let (u,v) be the Euclidean inner product on R², and let u = (2, -1), v = (-1,3), w =
(0,-5) and k = -3. Verify that
(a) (u,v) = (v₂u)
(b) (u + v, w) = (u,w) + (v,w)
(c) (ku,v) k(u,v)
=
Transcribed Image Text:INNER PRODUCT SPACES 1. Let (u,v) be the Euclidean inner product on R², and let u = (2, -1), v = (-1,3), w = (0,-5) and k = -3. Verify that (a) (u,v) = (v₂u) (b) (u + v, w) = (u,w) + (v,w) (c) (ku,v) k(u,v) =
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