Let W be a subspace of R4 spanned by the set Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}. (i) Show that Q is a basis of W. (ii) Does the vector u = (-3,2,5, 5) belong to space W? If that is the case, find the coordina vector of u relative to basis Q.
Let W be a subspace of R4 spanned by the set Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}. (i) Show that Q is a basis of W. (ii) Does the vector u = (-3,2,5, 5) belong to space W? If that is the case, find the coordina vector of u relative to basis Q.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 12CM
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![Let W be a subspace of R4 spanned by the set
Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}.
(i) Show that Q is a basis of W.
(ii) Does the vector u = (-3,2,5, 5) belong to space W? If that is the case, find the coordinate
vector of u relative to basis Q.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0602eaa-79a9-4455-9bd8-2642a3c0ae64%2F342cce40-b17e-4b9c-890d-0a2f1dc271c1%2Fv6iqqm_processed.png&w=3840&q=75)
Transcribed Image Text:Let W be a subspace of R4 spanned by the set
Q = {(1, 1, 3, 1), (1, 2,−1, 1), (1, 1, 0, -1)}.
(i) Show that Q is a basis of W.
(ii) Does the vector u = (-3,2,5, 5) belong to space W? If that is the case, find the coordinate
vector of u relative to basis Q.
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