Use-the-inner-product-f-g-10f-x-g-x-dx-in-the-vector-space-C0-0-1-of-continuous-functions-on-the-domain-0-1-to-find-the-orthogonal-projection-of-f-x-3×2-2-onto-the-subspace-V-spanned-by-g-x-

Question Number 138075 by Caroline last updated on 09/Apr/21

$$ \\ $$Use the inner product

⟨f,g⟩=∫10f(x)g(x)dx

in the vector space C0[0,1] of continuous functions on the domain [0,1] to find the orthogonal projection of f(x)=3×2−2 onto the subspace V spanned by g(x)=x and h(x)=1. (Caution: x and 1 do not form an orthogonal basis of V.)

projV(f)=  .

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