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

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 64E

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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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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