For all v € V, let : V' → F be defined by (p) = y(v) for y € V'. (a) Show that is linear, i.e. € V", where V" is defined to be (V')'. (b) Prove that the map Þ: V → V”" defined by Þ(v) — is an isomorphism. =
For all v € V, let : V' → F be defined by (p) = y(v) for y € V'. (a) Show that is linear, i.e. € V", where V" is defined to be (V')'. (b) Prove that the map Þ: V → V”" defined by Þ(v) — is an isomorphism. =
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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Transcribed Image Text:For all v € V, let : V' → F be defined by (4) = y(v) for 4 € V'.
(a) Show that is linear, i.e. û € V", where V" is defined to be (V')'.
(b) Prove that the map Þ: V → V" defined by Þ(v) — is an isomorphism.
=
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