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(b) On R2, the function (v, w) =v1W1+vịw2+v2w1+ V2W2. %3D

(b) On R2, the function (v, w) =v1W1+vịw2+v2w1+ V2W2. %3D

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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b, c, and e only. Thank You!

cise 1.3.25). solutions to starred exercises on page 454 1.3.3 Determine which of the following functions are inner products. *(a) On R2, the function (G) (v,w)=v1W1+vịw2+v2W2. %3D (b) On R2, the function (v, w) =v1W1 +vịw2+v2W1+v2w2. %3D (c) On R2, the function (v, w)33v1W1 +vịw2+v2W1+3v2w2. *(d) On Mn, the function (A, B) = tr(A* +B). (e) On P2, the function %3D (ax²+bx+c,dx²+ ex+ f) 3 ad+ be+cf. %3D *(f) On C[-1,1], the function f(x)g(x) X – I^= (8') 1.3.4 Determine which of the following statements are (f,8) dx. -1 V1-x %3D true and which are false
Transcribed Image Text:cise 1.3.25). solutions to starred exercises on page 454 1.3.3 Determine which of the following functions are inner products. *(a) On R2, the function (G) (v,w)=v1W1+vịw2+v2W2. %3D (b) On R2, the function (v, w) =v1W1 +vịw2+v2W1+v2w2. %3D (c) On R2, the function (v, w)33v1W1 +vịw2+v2W1+3v2w2. *(d) On Mn, the function (A, B) = tr(A* +B). (e) On P2, the function %3D (ax²+bx+c,dx²+ ex+ f) 3 ad+ be+cf. %3D *(f) On C[-1,1], the function f(x)g(x) X – I^= (8') 1.3.4 Determine which of the following statements are (f,8) dx. -1 V1-x %3D true and which are false
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Introduction:

A dot product (v,w) is called an inner product, when it follows the below three axioms:

(i) Linearity: au+bv,w=a(u,w)+b(v,w)

(ii) symmetric v,w=(w,v)

(iii) Positive definite: For any v∈V, v,v≥0 and v,v=0 if and only if v=0.

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