4. Let W be a vector subspace of a real inner product space V. Which of the following sets is not a vector space? (a) The set theoretic complement of W in V, i.e., the set of vectors of V that are not in W. (b) The orthogonal complement of W, relative to an inner product on V. (c) The set of linear transformations from V to W. (d) The set of linear transformations from V to V that map W to itself.
4. Let W be a vector subspace of a real inner product space V. Which of the following sets is not a vector space? (a) The set theoretic complement of W in V, i.e., the set of vectors of V that are not in W. (b) The orthogonal complement of W, relative to an inner product on V. (c) The set of linear transformations from V to W. (d) The set of linear transformations from V to V that map W to itself.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. Let W be a vector subspace of a real inner product space V. Which of the following sets is not
a vector space?
(a) The set theoretic complement of W in V, i.e., the set of vectors of V that are not in W.
(b) The orthogonal complement of W, relative to an inner product on V.
(c) The set of linear transformations from V to W.
(d) The set of linear transformations from V to V that map W to itself.
(e) The set of invertible linear transformations from V to itself.
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