Suppose v1, V2, V3 is an orthogonal set of vectors in R'. Let w be a vector in span(v1, v2, V3)such that(V1, V1)12, (v2, v2) = 26, (v3, V3) = 9,(w, v1) = 12, (w, v2) = -130, (w, v3) = 36,V2+then w =V1+V3 .1Use the inner product < f, g >=f(x)g(x)dx in the vector space C°[0, 1] to find theorthogonal projection of f(x) = 2x² – 5 onto the subspace V spanned by g(x)= x - and h(x) = 1.%3Dprojy (f) =

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Suppose v1, V2, V3 is an orthogonal set of vectors in R. Let w be a vector in span(v1, v2, V3) such that (V1, V1 ) = 12, (v2, V2 ) = 26, (v3, V3 ) = 9, (w, v¡) = 12, (w, V2 ) = -130, (w, v3) = 36, V2+ then w = V1+ V3 .

Suppose v1, V2, V3 is an orthogonal set of vectors in R. Let w be a vector in span(v1, v2, V3) such that (V1, V1 ) = 12, (v2, V2 ) = 26, (v3, V3 ) = 9, (w, v¡) = 12, (w, V2 ) = -130, (w, v3) = 36, V2+ then w = V1+ V3 .

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 87E

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Question

Suppose v1, V2, V3 is an orthogonal set of vectors in R'. Let w be a vector in span(v1, v2, V3)
such that
(V1, V1)
12, (v2, v2) = 26, (v3, V3) = 9,
(w, v1) = 12, (w, v2) = -130, (w, v3) = 36,
V2+
then w =
V1+
V3 .
1
Use the inner product < f, g >=
f(x)g(x)dx in the vector space C°[0, 1] to find the
orthogonal projection of f(x) = 2x² – 5 onto the subspace V spanned by g(x)
= x - and h(x) = 1.
%3D
projy (f) =

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