LetConsider the inner productf(x) = -5, g(x)=5a+2 and h(x)=2x².(p,q) = ˜ p(x)q(x) dzin the vector space P7 of polynomials of degree at most 7. Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of P7 spanned by the functions f(x), g(x), and h(x).{000} Let W be the subspace of R³ spanned by the vectorsFind the matrix A of the orthogonal projection onto W.A =-2 and -8-~-

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Answered: Let Consider the inner product f(x) =…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 45EQ

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Similar questions

Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector space?
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Find a basis for R2 that includes the vector (2,2).
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
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Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy -plane. Let T denote the linear operator mapping each vector into its orthogonal projection on the xy -plane. Then T(-8,5,7) = ( Ma )
Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.

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