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Which of the following statements are true? Select all true answers. If S is a subset but not a subspace of the vector space V , still then span (S)s a subspace of V. |{0}is the only trivial subspace of the vector space V. span (S)s always the smallest subset of the vector space V containing the set S. If S = span (Sthen S must be a subspace of the vector space V . If there is a linear combination of some proper subset of S to form the zero vector, then it must be linearly independent.

Which of the following statements are true? Select all true answers. If S is a subset but not a subspace of the vector space V , still then span (S)s a subspace of V. |{0}is the only trivial subspace of the vector space V. span (S)s always the smallest subset of the vector space V containing the set S. If S = span (Sthen S must be a subspace of the vector space V . If there is a linear combination of some proper subset of S to form the zero vector, then it must be linearly independent.

Advanced Engineering Mathematics
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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Which of the following statements are true? Select all true answers. | If S is a subset but not a subspace of the vector space V , still then span (S)s a subspace of V. {0} is the only trivial subspace of the vector space V. span (S)s always the smallest subset of the vector space V containing the set S. If S span (Sthen S must be a subspace of the vector space V. | If there is a linear combination of some proper subset of S to form the zero vector, then it must be linearly independent.
Transcribed Image Text:Which of the following statements are true? Select all true answers. | If S is a subset but not a subspace of the vector space V , still then span (S)s a subspace of V. {0} is the only trivial subspace of the vector space V. span (S)s always the smallest subset of the vector space V containing the set S. If S span (Sthen S must be a subspace of the vector space V. | If there is a linear combination of some proper subset of S to form the zero vector, then it must be linearly independent.
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