Let W be the subspace spanned by u, and u,. Write y as the sum of a vector in W and a vector orthogonal to W.13- 1yu1, u2 =14·14.....O A.В.- 1115y =10y =106.- 86.20D.1149.y =10- 7y =20- 17122+2.+COCOC.

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Answered: Let W be the subspace spanned by u, and…

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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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.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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 projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
Let U and W be arbitrary subspaces in vector space V with dimensions dim U=6 and dimW=4. Which of the following conclusions is not correct? (a) If dimV=9, then dim(U∩W)≥1. (b) If dim(U∩W)=3, then dim(U+W)=7. (c) If dim(U+W)=6, then W⊆U. (d) If dim(U∩W)=4, then W⊆U. (e) If dimV=12, then U∩W={0}.
Find the projection of the vector v onto the subspace S.
Which of the listed pairs has the set U as a vector subspace of the vector space V?
Find the orthogonal projection of v=(−19,6,18)onto the subspace W of ℝ3 spanned by (−7,6,−2) and (0,6,18) ProjW(v)=
Show that the set of vectors {(−4, 1, 3), (5, 1, 6), (6, 0, 2)} does not span R3, but that it does span the subspace of R3 consisting of all vectors lying in the plane with equation x + 13y − 3z = 0.
Consider the subspace W of R4 spanned by the set S and a vector v in the attachment, and please solve (1) - (3). Thank you!

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Let W be the subspace spanned by u, and uz. Write y as the sum of a vector in W and a vector orthogonal to W. 13 2 - 1 y = 3 u, = 2 U2 3 14 - 1 4 ..... O A. В. 2 - 11 2 15 y = 10 7 10 13 + y = - 8 20 OC. D. 2 11 4 9 y = 10 - 7 y = 20 - 17 8 12 + L. +