Use least squares to find the orthogonal projection of u onto the subspace of R spanned by the vectors v1, v2, andwhereV3.u = (0, 2, 8, 0), v1 = (3, 0, 0, 1), v2 = (0, 1, –1, 0), V3 = (1, 1, 0, -3).%3D

First we will choose an arbitrary linear combination of the vectors v1, v2, v3 to represent u. From…

Answered: Use least squares to find the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 40EQ

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Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). 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 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.
Find the bases for the four fundamental subspaces of the matrix. A=[010030101].
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
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 least squares to find the orthogonal projection of u onto the subspace of R* spanned by the vectors v1, v2, and V3. where u = (0, 2, 8, 0), vị = (3, 0, 0, 1), v2 = (0, 1, –1, 0), v3 = (1, 1, 0, –3).