3940Question 6Which of the following is a subspace of R3?O A. S = { (x,y,z) ER|x-y=1}O B. U = { (x,y,z) ER | y=x2)-OC. None of the choices in the list.O D. V = { (x,y,z) ERz=1)-O E. W = {(x.y.z) ER |y=V-3}13D

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Answered: Question 6 Which of the following is a…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 62E: Spanning the Same Subspace In Exercises 61and 62, show that the sets S1and S2span the same subspace...

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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.
In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. V=Mnn,WAinMnn:detA=1
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.
Spanning the Same Subspace In Exercises 61and 62, show that the sets S1and S2span the same subspace of R3. S1={(0,0,1),(0,1,1),(2,1,1)} S2={(1,1,1),(1,1,2),(2,1,1)}
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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Question 6 Which of the following is a subspace of R3? O A. S= ((x,y,z) ER |x-y=1} O B. U = { (x,y,z) ER | y=x?)- O C. None of the choices in the list. O D. V = { (x,y.z) ER z=1) O E. W ={(x.y.2) ER | y=V23}