b, c, and e only. Thank You! cise 1.3.25).solutions to starred exercises on page 4541.3.3 Determine which of the following functions are innerproducts.*(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 functionf(x)g(x)X – I^= (8')1.3.4 Determine which of the following statements are(f,8)dx.-1 V1-x%3Dtrue and which are false

Answered: (b) On R2, the function (v, w)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.1: Polynomial Functions Of Degree Greater Than

Problem 12E

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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

Expert Solution

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Note: Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.

Introduction:

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

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

(ii) symmetric $(v, w) = (w, v)$

(iii) Positive definite: For any $v \in V$ , $(v, v) \geq 0$ and $(v, v) = 0$ if and only if $v = 0$ .

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