Defining a statement (Vector Algebra)

AI Thread Summary
The discussion focuses on defining the concept of a spanning set in vector algebra. It clarifies that the statement "the set {v1, v2,..., vn} spans V" indicates that any vector in the vector space V can be expressed as a linear combination of the vectors in the set. The conversation highlights the importance of understanding linear dependence and independence, noting that more information about the vector space is needed to determine these properties. It also suggests that the definition of "span" should be referenced from the textbook. Ultimately, the key takeaway is that the set must cover the entire vector space through linear combinations.
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Homework Statement



Let V be a vector space over the field F. Define what is meant by the statement
"For vectors v1, v2,...,vn belonging to V, the set {v1,v2,...,vn} spans V

Homework Equations



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The Attempt at a Solution



Does it mean that the set is linearly dependent?
 
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You can't tell whether the vectors are linearly dependent or linearly independent without knowing more about your vector space V.

Doesn't your book have a definition of the term "span"?
 
So it is a spanning set for V?
 
The problem tells you that this set spans V. You are supposed to say what this means.
 

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