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) is a subspace of V. {0}is the only trivial subspace of the vector space V. span (S) is always the smallest subset of the vector space V containing the set S. If S = span (S)then 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
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) is a subspace of V. {0}is the only trivial subspace of the vector space V. span (S) is always the smallest subset of the vector space V containing the set S. If S = span (S)then 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
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 37E: Let V be the set of all positive real numbers. Determine whether V is a vector space with the...
Related questions
Question
![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) is a subspace of V.
{0}is the only trivial subspace of the
vector space V .
span (S) is always the smallest
subset of the vector space V
containing the set S.
If S = span (S)then S must be a
subspace of the vector space V.
%3D
If there is a linear combination of
some proper subset of S to form the
zero vector, then it must be linearly
independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31c1e17c-1f45-4807-97e0-197cb494848e%2Fb32e812d-ef42-4676-93fa-d17c7438ea49%2Fgjzzn8j_processed.jpeg&w=3840&q=75)
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) is a subspace of V.
{0}is the only trivial subspace of the
vector space V .
span (S) is always the smallest
subset of the vector space V
containing the set S.
If S = span (S)then S must be a
subspace of the vector space V.
%3D
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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