1Let S be the subspace of R° spanned by the vectors1and | 213, and let b3Find the point in S that is closest to b.(If the entries of your vector do not come out as whole numbers, roundthem to 4 decimal places.) Let S be the subspace of R° spanned by the vectorsand224Find the matrix P for the orthogonal projection onto S.(If the entries of your matrix do not come out as whole numbers, roundthem to 4 decimal places.)

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Answered: 1 1 Let S be the subspace of R° spanned…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 26EQ

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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.
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In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In each case either prove that S forms a subspace of 2 or give a counterexample to show that it does not. xy0
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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.
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1 1 Let S be the subspace of R° spanned by the vectors and 2 4 3 and let b 3 Find the point in S that is closest to b. 5 (If the entries of your vector do not come out as whole numbers, round them to 4 decimal places.)