please send handwritten solution for part b {[:}5. (a) Consider the subspace W = spanand consider the vector-11u =-1|. Find the vector w in W such that w is the closest vector to u.-1(b) How far is w from u?

You asked to solve part(b) only.

Answered: please send handwritten solution for…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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.
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.
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of 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 a basis for the subspace given by the plane −3x + 2y + 5z = 0.
Consider the vector subspaces U, V ,W ⊆ Rn such that U ⊆ V ⊆ W. If dimU = 5 and dimW = 7, what can be said about V? -It always contains a set of 5 linearly independent vectors -dimV = 6 -it always contains a set of 7 linearly independent vectors -the zero vector is not contained in it -it contains a non-zero vector
Write the equation of a subspace that passes through a point a ∈ R^d and isorthogonal to a given vector b. What is that equation for d = 3, d = 2?
what is the dimension of the subspace H knowing that it is not independent

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