Answered: Use the inner product < f,g >= 0…

Use the inner product < f,g >= 0 f(z)g(z)da in the vector space Cº[0, 1] to find the orthogonal projection of f(x) = 4x² - 4 onto the subspace V spanned by g(x) ==-- and h(z)=1. projy(f)=

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 12E

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Linear algebra. Will thumbs up if correct

Use the inner product<f,g>=
f(a)g(x)da in the vector space Cº[0, 1] to find the
orthogonal projection of ƒ(z) = 42² – 4 onto the subspace V spanned by g(¹) == −/and
h(x)=1.
projy(f)
=

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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