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3. For each of the following inner product spaces V and linear operators T on V, evaluate T* at the given vector in V. (a) VR2, T(a, b) = (2a + b, a 3b), x = (3, 5). (b) V = C², T(21, 22) = (221 + iz2, (1 − i)z1), x = (3 — i, 1 + 2i). - (c) V=P₁(R) with (f,g) = {* f(t)g(t) dt, T(f) = ƒ' +3f, f(t)=4-2t

3. For each of the following inner product spaces V and linear operators T on V, evaluate T* at the given vector in V. (a) VR2, T(a, b) = (2a + b, a 3b), x = (3, 5). (b) V = C², T(21, 22) = (221 + iz2, (1 − i)z1), x = (3 — i, 1 + 2i). - (c) V=P₁(R) with (f,g) = {* f(t)g(t) dt, T(f) = ƒ' +3f, f(t)=4-2t

Advanced Engineering Mathematics
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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3. For each of the following inner product spaces V and linear operators T on V, evaluate T* at the given vector in V. (a) VR2, T(a, b) = (2a + b, a 3b), x = (3, 5). (b) V = C², T(21, 22) = (221 + iz2, (1 − i)z1), x = (3 — i, 1 + 2i). - (c) V=P₁(R) with (f,g) = {* f(t)g(t) dt, T(f) = ƒ' +3f, f(t)=4-2t
Transcribed Image Text:3. For each of the following inner product spaces V and linear operators T on V, evaluate T* at the given vector in V. (a) VR2, T(a, b) = (2a + b, a 3b), x = (3, 5). (b) V = C², T(21, 22) = (221 + iz2, (1 − i)z1), x = (3 — i, 1 + 2i). - (c) V=P₁(R) with (f,g) = {* f(t)g(t) dt, T(f) = ƒ' +3f, f(t)=4-2t
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